A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Survey on algebraic K- and L-theory conjecture.
Finite presentations for skein algebras linked to gauge field theory.
We introduce two -theories, one for vector bundles whose fibers are modules of vertex operator algebras, another for vector bundles whose fibers are modules of associative algebras. We verify the cohomological properties of these -theories, and construct a natural homomorphism from the VOA K-theory to the associa…
It is well-known that classical two-dimensional topological field theories are in one-to-one correspondence with commutative Frobenius algebras. An important extension of classical two-dimensional topological field theories is provided by open-closed two-dimensional topological field theories. In this paper we extend o…
Develops differential K-theory for noncommutative algebras.
This paper investigates the relationship between algebraic quantum field theories and factorization algebras on globally hyperbolic Lorentzian manifolds. Functorial constructions that map between these two types of theories in both directions are developed under certain natural hypotheses, including suitable variants o…
Machine learning explores symmetries in field theory and algebra.
Quantum field theory uses Lorentzian bordisms to describe time evolution.
Floer homology connects to quiver Hecke algebras in Coulomb branches.
This study introduces a unified cohomology theory for braided algebras.
The abstract discusses connecting quantum mechanics and algebraic index theories.
In this thesis, we introduce a new cohomology theory associated to a Lie 2-algebras and a new cohomology theory associated to a Lie 2-group. These cohomology theories are shown to extend the classical cohomology theories of Lie algebras and Lie groups in that their second groups classify extensions. We use this fact to…
Study K-theory of Etesi -algebras to understand smooth manifolds.
Algebraic treatment of connection reduction over a special disc.
In this article, we introduce a new cohomology theory associated to a Lie 2-algebras. This cohomology theory is shown to extend the classical cohomology theory of Lie algebras; in particular, we show that the second cohomology group classifies an appropriate type of extensions.
The paper studies properties of stated SL(n)-skein algebras and their centers.
We expand Topological Field Theory on some special CW-complexes (brane complexes). This Brane Topological Field Theory one-to-one corresponds to infinite dimensional Frobenius Algebras, graduated by CW-complexes of lesser dimension. We define general and regular Hurwitz numbers of brane complexes and prove that they ge…
Maximal Laplacian algebras applied to invariant theory solved inverse problems.
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 …
Jones polynomials derived from K-theory of a cluster algebra.
Develops a bialgebra theory for post-Lie algebras using geometric interpretations and bilinear forms.
Paper reviews algebraic research in machine learning theory.
Distributivity in algebraic structures appeared in many contexts such as in quasigroup theory, semigroup theory and algebraic knot theory. In this paper we give a survey of distributivity in quasigroup theory and in quandle theory.
This is the first in a series of papers laying the foundations for a differential graded approach to derived differential geometry (and other geometries in characteristic zero). In this paper, we study theories of supercommutative algebras for which infinitely differentiable functions can be evaluated on elements. Such…
Abstract: Geometrically reformulates estimation theory for finite-dimensional C*-algebras.
The paper explores handlebody versions of various diagram algebras.
Lie algebroids and curved Lie algebras are equivalent categories.
This thesis explores DAHA representations using stated skein theory.
In GT/0006019 oriented quantum algebras were motivated and introduced in a natural categorical setting. Invariants of knots and links can be computed from oriented quantum algebras, and this includes the Reshetikhin-Turaev theory for Ribbon Hopf algebras. Here we continue the study of oriented quantum algebras from a m…
Researchers prove positivity of skein algebra structure constants for specific surfaces.
Proves super-version of index theorem from algebraic cobordism invariants.
This work is devoted to an intrinsic cohomology theory of Koszul-Vinberg algebras and their modules. Our results may be regarded as improvements of the attempt by Albert Nijenhuis in [NA]. The relationships between the cohomology theory developed here and some classical problems are pointed out, e.g. extensions of alge…
This paper revisits Differential Galois Theory using Hopf algebras for Lie pseudogroups.
In this paper, we prove the algebraic K-theory Novikov conjecture for group algebras over the ring of Schatten class operators. The main technical tool in the proof is an explicit construction of the Connes-Chern character.
In this thesis, we study deformations of compact holomorphic Poisson manifolds and algebraic Poisson schemes in the framework of Kodaira-Spencer's analytic deformation theory and Grothendieck's algebraic deformation theory.
Study algebraic K-theory for specific groups of non-orientable surfaces.
We give a concise introduction to the Farrell-Jones Conjecture in algebraic -theory and to some of its applications. We survey the current status of the conjecture, and we illustrate the two main tools that are used to attack it: controlled algebra and trace methods.
We explain how deformation theories of geometric objects such as complex structures, Poisson structures and holomorphic bundle structures lead to differential Gerstenhaber or Poisson algebras. We use homological perturbation theory to obtain algebra structures and some canonically defined deformations of s…
New algebraic geometry and statistical manifold connections proven.
The thesis explores centralisers and Hecke algebras in representation theory with applications to knots and physics.
There is an interpretation of open string field theory in algebraic topology. An interpretation of closed string field theory can be deduced from this open string theory to obtain as well the interpretation of open and closed string field theory combined.
Rewriting theory applied to diagrammatic algebras for categorification.
We redefine the cord algebra, which was introduced by Lenhard Ng as a topological knot invariant, in terms of Morse Theory. The determination of the cord algebra of the unknot and of the righthanded trefoil are given. We proove that the cord algebra in our definition is a knot invariant.
Develops quantum character theory for complex reductive groups.
Let be a word hyperbolic group. We prove that the algebraic -theory groups of $\dbZ [G]$, $K_n(\dbZ[G])$, have finite rank for all $n\in \dbZ$. For a few classes of groups, we give explicit formulas for the ranks of the algebraic -theory groups of their group rings.
Homology theories for associative algebraic structures are well established and have been studied for a long time. More recently, homology theories for self-distributive algebraic structures motivated by knot theory, such as quandles and their relatives, have been developed and investigated. In this paper, we study ass…
Revives Vogel's diagrammatic technique for universal Lie algebra computations.
We construct a new equivariant cohomology theory for a certain class of differential vertex algebras, which we call the chiral equivariant cohomology. A principal example of a differential vertex algebra in this class is the chiral de Rham complex of Malikov-Schechtman-Vaintrob of a manifold with a group action. The ma…