Finite rank proven for algebraic K-theory groups of hyperbolic groups.
problem Determining the finite rank of algebraic K-theory groups of hyperbolic groups.
method Proved finite rank for algebraic K-theory groups of Z[G] for all n∈Z, provided explicit formulas for some groups. result Finite rank proven for algebraic K-theory groups of hyperbolic groups.
We expose a K-theoretic approach to study group C*-algebras and C*-algebraic compact quantum groups: 1. The conception of multidimensional geometric quantization and the index of group C*-algebras; 2. the entire homology of noncommutative de Rham currents and the noncommutative Chern characters, and their computation f…
Computes the component group of arbitrary real algebraic groups.
problem Computing the component group of arbitrary real algebraic groups.
method Structure results on algebraic groups and Galois cohomology methods.
result The group of connected components π0G(R) is an elementary Abelian 2-group. Survey on algebraic K- and L-theory conjecture.
problem Algebraic K- and L-theory of groups rings.
method Not specified in the abstract, likely involves algebraic and geometric approaches.
result Applications to algebra, geometry, group theory, and topology.
The paper examines formality properties of finitely generated groups and Lie algebras.
problem Formality properties of finitely generated groups and Lie algebras.
method Analysis of various Lie algebras attached to groups, including Malcev, graded, and holonomy Lie algebras, and their behavior under different algebraic operations.
result The 1-minimal model of the group and Taylor expansions provide key tools to understand formality properties.
Characterizes Lie groups of automorphisms of cotangent bundles of Lie groups.
problem Characterizing Lie groups of automorphisms of cotangent bundles of Lie groups.
method Completely characterizes Lie groups of automorphisms of cotangent bundles of Lie groups using various methods.
result Lie groups of automorphisms of cotangent bundles of Lie groups are super symmetric Lie groups.
Introduces Hom-Lie groups and their integrability, defining Hexp map and adjoint representation.
problem Integrability of Hom-Lie algebras and associated Hom-Lie groups.
method Definition of Hom-Lie groups and algebras, integration of Hom-Lie algebras, Hexp map definition.
result Every regular Hom-Lie algebra is integrable, Hexp map is universal.
Isomorphic algebra connects Toeplitz to Heisenberg group.
problem Connecting Toeplitz algebra to Heisenberg group.
method Isomorphism between Toeplitz algebra and Heisenberg group ideal.
result Found isomorphism between algebra and Heisenberg group ideal.
Survey on algebraic fibers of group extensions and their finiteness properties.
problem Existence and finiteness of algebraic fibers in group extensions.
method Analysis of abstract and pro-p groups. result Finiteness properties of algebraic fibers in group extensions.
Study extends JB-algebra structure group results to infinite dimensions.
problem Extend results for real Jordan algebras to infinite dimensional JB-algebras.
method Prove structure groups, cone preserving groups, and automorphism groups are embedded Banach-Lie groups; describe components via cones, isotopes, and central projections; apply to special JB-algebra of self-adjoint operators.
result Full description of components of structure group and automorphism group, including their Banach-Lie algebras and connected components.
The paper studies gradings on nilpotent Lie algebras linked to smooth algebraic varieties.
problem Understanding gradings on nilpotent Lie algebras associated with algebraic varieties.
method Analyzing lattice structures in nilpotent Lie groups and their fundamental groups.
result Conditions for a lattice to be the fundamental group of a smooth complex algebraic variety.
The paper explores geometric and algebraic structures on Lie groups.
problem Investigating F-manifolds and Fextman-algebras on Lie groups. method Constructing a canonical connection and analyzing curvature and holonomy.
result Established the integrability of a Poisson-algebra distribution.
Study classifies algebraic solitons on 3D Lie groups.
problem Classifying solitons on Lie groups.
method Investigated cross curvature flow and second order renormalization group flow.
result Complete classification of left invariant algebraic solitons.
Study recovers C*-algebra from fields of Toeplitz algebras on specific groups.
problem Recovering C*-algebra from fields of Toeplitz algebras on specific groups.
method Using continuous fields of Toeplitz algebras and a crossed product.
result Algebra of principal symbols can be recovered from fields of Toeplitz algebras.
Profinite rigidity studied for algebraic fibring of groups.
problem Profinite rigidity of groups through algebraic fibring.
method Introducing TAP groups and proving algebraic fibring is a profinite property.
result Algebraic fibring is a profinite property for LERF groups.
Generalizes group cohomology and holonomy Lie algebra computations.
problem Computing cup-products and holonomy Lie algebras for arbitrary groups.
method Explicit formula for cup-products, Magnus expansion method for holonomy Lie algebras.
result Explicit formula for cup-products in cohomology of 2-complexes.
Study of Lie algebras linked to graphs, revealing symmetry groups.
problem Understanding symmetries in Lie algebras associated with graphs.
method Analyzing 2-step nilpotent Lie algebras linked to uniform complete graphs.
result The Lie automorphism group includes the dihedral group of order 2n. Homology of partition algebras matches symmetric group homology under certain conditions.
problem Understanding homology of partition algebras and comparing it to symmetric groups.
method Inductive resolution and high acyclicity arguments, parallel to earlier work on Brauer algebras.
result Homology of partition algebras is isomorphic to symmetric group homology under specific conditions.
It is shown that there is a C∗-algebraic quantum group related to any double Lie group. An algebra underlying this quantum group is an algebra of a differential groupoid naturally associated with a double Lie group
The paper calculates automorphisms of Weil algebras, focusing on one-component groups.
problem Calculating automorphisms of Weil algebras.
method Direct calculation method detailed for R-algebra automorphisms. result Two cases of determinant values for linear part of one-component groups.
Witt algebra acts on categorified quantum groups in type A.
problem Action of Witt algebra on categorified quantum groups.
method Construction of action on categorified quantum group and foams.
result Action of Witt algebra on foams recovers previous results.
Introduces new cohomology theories for Lie 2-algebras and groups.
problem Classical cohomology theories do not extend to Lie 2-algebras and groups.
method Develops new cohomology theories and uses them to prove integrability.
result New cohomology theories classify extensions and prove integrability of Lie 2-algebras.
The paper connects Brauer algebra homology to symmetric group homology.
problem Understanding the homology of Brauer algebras.
method Interpreting Brauer algebras as Tor-groups and comparing to symmetric group homology.
result Isomorphism of homology groups under specific conditions.
Study braid groups in handlebodies and introduce a new algebra.
problem Kernel of braid group homomorphism in handlebodies.
method Prove kernel as semi-direct product of free groups and introduce algebra.
result Kernel of braid group homomorphism is a semi-direct product of free groups.
Homologies of Jones and partition algebras match cyclic and symmetric groups.
problem Matching homologies of specific algebras to cyclic and symmetric groups.
method Proving isomorphisms between algebras' homologies and group homologies.
result Homologies of Jones and partition algebras are isomorphic to cyclic and symmetric groups.
Study algebraic K-theory for specific groups of non-orientable surfaces.
problem Algebraic K-theory of group rings for specific non-orientable surface groups.
method Detailed analysis of group rings and algebraic K-theory.
result General formula for algebraic K-theory groups of mapping class groups of non-orientable surfaces.
Study expanding solitons on complex Lie groups with specific algebraic structures.
problem Investigate expanding solitons on complex Lie groups with left-invariant metrics.
method Analyze the algebraic structure of complex Lie groups and their decompositions.
result Show that the Lie algebras of complex Lie groups decompose into semidirect products.
New groups found that don't virtually algebraically fiber, related to mapping class group orbits.
problem Existence of finite orbits for higher Prym representations of the mapping class group.
method Study of surface-by-surface and surface-by-free groups.
result Existence of free-by-free and free-by-surface groups that do not algebraically fiber.
The paper integrates Lie 2-algebra derivations into automorphism groups.
problem Integrating Lie 2-algebra derivations into a more structured form.
method Constructing the automorphism 2-group of a Lie 2-algebra.
result The automorphism 2-group integrates the derivation Lie 2-algebra.
Formulas for algebraic K-theory groups of Hilbert modular group derived from finite subgroups.
problem Computing algebraic K-theory groups of Hilbert modular group.
method Formulas derived from maximal finite subgroups.
result Formulas for Whitehead groups and rational K-theory groups.
Lie's Third Theorem, asserting that each finite-dimensional Lie algebra is the Lie algebra of a Lie group, fails in infinite dimensions. The modern account on this phenomenon is the integration problem for central extensions of infinite-dimensional Lie algebras, which in turn is phrased in terms of an integration proce…
In this paper, we present a study on the prolongations of representations of Lie algebras. We show that a tangent bundle of a given Lie algebra attains a Lie algebra structure. Then, we prove that this tangent bundle is algebraically isomorphic to the Lie algebra of a tangent bundle of a Lie group. Using these, we defi…
New groups algebraically fibre with high-dimensional hyperbolic groups.
problem Finding new quasi-isometry classes of hyperbolic groups.
method Constructing infinitely many hyperbolic groups as finite-index subgroups of right-angled Coxeter groups.
result Groups algebraically fibre with finitely presented kernels, expanding finiteness properties.
Our paper is devoted to the study of the holonomy groups of Finsler surfaces using the methods of infinite dimensional Lie theory. The notion of infinitesimal holonomy algebra will be introduced, by the smallest Lie algebra of vector fields on an indicatrix, containing the curvature vector fields and their horizontal c…
These lectures given in Montreal in Summer 1997 are mainly based on, and form a condensed survey of, the book by N. Chriss and V. Ginzburg: `Representation Theory and Complex Geometry', Birkhauser 1997. Various algebras arising naturally in Representation Theory such as the group algebra of a Weyl group, the universal …
New method computes automorphisms of surface groups using skein algebras.
problem Computing automorphisms of surface groups.
method Using skein algebras and Goldman Lie algebra.
result Refined formula for automorphisms of homology cylinders.
New algebraic fundamental groups identified for fake projective planes.
problem Characterizing algebraic fundamental groups of fake projective planes.
method Analysis of complex conjugate pairs and explicit finite étale covers.
result Forty-six distinct isomorphism classes of algebraic fundamental groups.
Builds geometric structures for algebraic groups over real closed fields.
problem Characterizing and decomposing algebraic groups over specific valued fields.
method Real algebraic geometry to construct and analyze affine buildings.
result Computed stabilizers and obtained group decompositions.
Abstract: Connections between Lie algebras and symplectic nilmanifolds explored.
problem Understanding the relationship between Lie algebras and symplectic nilmanifolds.
method Central extensions of Lie algebras, dynamical systems, and symplectic nilmanifolds constructed.
result Covering Lie groups for symplectic nilmanifolds can have any rank as solvable Lie groups.
Analogous exponential map defined for Hopf algebras.
problem Defining an exponential map for Hopf algebras.
method Analogy with Lie groups, interpretation as states, Hilbert C* bimodules, dual Hopf algebra elements.
result Multiple interpretations of exponential map values in Hopf algebras.
Study on pseudo-Riemannian algebraic Ricci solitons in 4D Lie groups.
problem Investigating conditions for pseudo-Riemannian algebraic Ricci solitons on 4D Lie algebras.
method Analyzing the algebraic Ricci soliton equation for each 4D Lie algebra.
result Complete description of pseudo-Riemannian algebraic Ricci solitons in dimension four.
The document provides tables of prehomogeneous and étale modules for reductive algebraic groups.
problem Classifying and tabulating prehomogeneous and étale modules for reductive algebraic groups.
method Classification and tabulation of prehomogeneous and étale modules based on existing work and the author's determination.
result Tables of prehomogeneous and étale modules for reductive algebraic groups with up to two simple factors.
The purpose of this paper is to show how central extensions of (possibly infinite-dimensional) Lie algebras integrate to central extensions of étale Lie 2-groups. In finite dimensions, central extensions of Lie algebras integrate to central extensions of Lie groups, a fact which is due to the vanishing of π_2 for each …
Solves a problem posed by Jones linking Hecke groups to subfactor indices.
problem Relation between Hecke groups and subfactor indices in von Neumann algebras.
method Using cluster C*-algebras.
result Solved the problem posed by V. F. R. Jones.
Investigates linearity of group amalgams and new examples of non-linear groups.
problem Linearity of group amalgams and examples of non-linear groups.
method Investigates linearity of amalgams of subgroups of algebraic groups.
result Establishes linearity of certain 'doubles' of linear groups and finds new non-linear examples.
Paper defines tangent Lie algebra for non-smooth subgroups of diffeomorphism groups.
problem Understanding tangent spaces of non-smooth subgroups of diffeomorphism groups.
method Introduced tangent Lie algebra TG for non-smooth subgroups of Diff(M) of a compact manifold M.
result Tangent Lie algebra TG is a Lie subalgebra of smooth vector fields on M.
Defines and classifies algebraic Schouten solitons in 3D Lorentzian Lie groups.
problem Classifying solitons in 3D Lorentzian Lie groups.
method Defined algebraic Schouten solitons and classified them for specific connections.
result Classified algebraic Schouten solitons for various connections on 3D Lorentzian Lie groups.
Develops deformed algebras and groups from formal series over groupoids, with applications to cobordism.
problem Formal series over groupoids for algebras and groups.
method Deformation along a family of indexes, formal series.
result Regular Frölicher Lie groups and sometimes Fréchet Lie groups.