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.
Lectures explore how differential methods improve understanding of algebraic group orbit spaces.
AIDN uses deep learning to represent algebraic structures.
We discuss the nature of structure-preserving maps of varies function algebras. In particular, we identify isomorphisms between special Colombeau algebras on manifolds with invertible manifold-valued generalized functions in the case of smooth parametrization. As a consequence, and to underline the consistency and vali…
Develops Lie algebraic approach for compact complex homogeneous manifolds.
We develop the idea of using an algebraic-geometry approach to classical differential geometry problems. Consider an orthogonal net constructed according to algebraic-geometric data we obtain a set of smooth orthogonal nets that are Ribaucour transformations of the initial orthogonal net.
Surveying probabilistic real algebraic geometry.
We develop the theory of linear algebra over a (Z_2)^n-commutative algebra (n in N), which includes the well-known super linear algebra as a special case (n=1). Examples of such graded-commutative algebras are the Clifford algebras, in particular the quaternion algebra H. Following a cohomological approach, we introduc…
Constructive approach to Lie algebra gradings, computing maximal and enumerating all gradings.
Study framizations of algebras using Schur--Weyl duality and tied braids.
The paper analyzes a simple neural network model with algebraic methods.
Unified approach to deform Lie-Hamilton systems using Poisson-Hopf algebra.
New bialgebra structures for relative Poisson algebras are introduced.
Constructs Lie-Rinehart algebra for Einstein's equations.
We explore the graded and filtered formality properties of finitely generated groups by studying the various Lie algebras over a field of characteristic 0 attached to such groups, including the Malcev Lie algebra, the associated graded Lie algebra, the holonomy Lie algebra, and the Chen Lie algebra. We explain how thes…
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…
Paper defines and computes a new weight system for gl_N Lie algebra.
In this study, we classify some soliton nilpotent Lie algebras and possible candidates in dimension 8 and 9 up to isomorphy. We focus on 1 < 2 < ::: < n type of derivations where n is the dimension of the Lie algebras. We present algorithms to generate possible algebra structures.
Algebraic geometry replaces manifolds in differential geometry.
We develop an approach to construct Poisson algebras for non-linear scalar field theories that is based on the Cahiers topos model for synthetic differential geometry. In this framework the solution space of the field equation carries a natural smooth structure and, following Zuckerman's ideas, we can endow it with a p…
Homological algebra used to study local equivalence of complex rings.
New algebraic approach for approximating Hamiltonian dynamics.
These notes have been prepared for the Workshop on "(Non)-existence of complex structures on ", to be celebrated in Marburg in March, 2017. The material is not intended to be original. It contains a survey about the smallest of the exceptional Lie groups: , its definition and different characterizati…
Develops quantum cluster algebra approach to solve tetrahedron equation.
New algebraic formalism for differential calculus in Diolic algebras.
The projective algebra p(M;F) (i.e the collection of all projective vector fields)of a Finsler space (M;F) is a finite-dimensional Lie algebra with respect to the usual Lie bracket. The projective algebra of Einstein metrics has been perpetually studied from physical and geometrical approaches. Here, the projective alg…
Automorphisms of finite order and real forms of "smooth" affine Kac-Moody algebras are studied, i.e. of 2-dimensional extensions of the algebra of smooth loops in a simple Lie algebra. It is shown that they can be parametrized by certain invariants and that in particular the classification of involutions essentially fo…
A novel geometric algebra-based KG embedding framework improves link prediction.
Possible irreducible holonomy algebras $\g\subset\sp(2m,\Real)$ of odd Riemannian supermanifolds and irreducible subalgebras $\g\subset\gl(n,\Real)$ with non-trivial first skew-symmetric prolongations are classified. An approach to the classification of some classes of the holonomy algebras of Riemannian supermanifolds…
Rewriting theory applied to diagrammatic algebras for categorification.
Study bi-graded Lie algebras and their applications.
The present paper is a short survey on the mathematical basics of Classical Field Theory including the Serre-Swan' theorem, Clifford algebra bundles and spinor bundles over smooth Riemannian manifolds, Spin^C-structures, Dirac operators, exterior algebra bundles and Connes' differential algebras in the commutative case…
Paper reviews algebraic research in machine learning theory.
Study of control problems on Carnot groups with SO(3) symmetry using geometric algebra.
Characterizes algebraic integrability and minimality of Lie equations for non-commutative pseudogroups.
We study the connections between link invariants, the chromatic polynomial, geometric representations of models of statistical mechanics, and their common underlying algebraic structure. We establish a relation between several algebras and their associated combinatorial and topological quantities. In particular, we def…
We extend the classical characterization of a finite-dimensional Lie algebra g in terms of its Maurer-Cartan algebra-the familiar differential graded algebra of alternating forms on g with values in the ground field, endowed with the standard Lie algebra cohomology operator-to sh Lie-Rinehart algebras. To this end, we …
New algebraic approach classifies conformally superintegrable systems in arbitrary dimensions.
New -algebra approach unifies machine learning strategies.
New invariant for singular links via bt-algebra.
Randomized Geometric Algebra for Convex Neural Networks Optimizes Transfer Learning.
Paper proves unique tangent maps for complex maps into algebraic varieties.
Given a unital associatve graded algebra we construct the graded q-differential algebra by means of a graded q-commutator, where q is a primitive N-th root of unity. The N-th power (N>1) of the differential of this graded q-differential algebra is equal to zero. We use our approach to construct the graded q-differentia…
A new approach to symbol calculus on filtered manifolds using -algebras.
This is the first paper in a series of eight where in the first three we develop a systematic approach to the geometric algebras of multivectors and extensors, followed by five papers where those algebraic concepts are used in a novel presentation of several topics of the differential geometry of (smooth) manifolds of …
Revives Vogel's diagrammatic technique for universal Lie algebra computations.
Unified determinants via a single equation.
Generalizations in many directions of the contraction procedure for Lie algebras introduced by E.J.Saletan are proposed. Products of arbitrary nature, not necessarily Lie brackets, are considered on sections of finite-dimensional vector bundles. Saletan contractions of such infinite-dimensional algebras are obtained vi…
If a Lie algebra structure g on a vector space is the sum of a family of mutually compatible Lie algebra structures g_i's, we say that g is simply assembled from the g_i's. Repeating this procedure with a number of Lie algebras, themselves simply assembled from the g_i's, one obtains a Lie algebra assembled in two step…