Related papers: Quantization on a Lie group: Higher-order Polariza…
This paper works as an appendix of the paper titled Geometry of Associated Quantum Vector Bundles and the Quantum Gauge Group and for paper titled Yang-Mills-Connes Theory and Quantum Principal SU(N)-Bundles. Here, we are going to prove…
For a stratified group $G$, we construct a class of polarised Lie groups, which we call modifications of $G$, that are locally contactomorphic to it. Vice versa, we show that if a polarised group is locally contactomorphic to a stratified…
Quantization is not a straightforward proposition, as shown by Groenewold's and Van Hove's discovery, more than fifty years ago, of an "obstruction" to quantization. Their "no-go theorems" assert that it is impossible to consistently…
A central extension of the loop group of a Lie group is called transgressive, if it corresponds under transgression to a degree four class in the cohomology of the classifying space of the Lie group. Transgressive loop group extensions are…
Generalized quantum cluster algebras introduced in [1] are quantum deformation of generalized cluster algebras of geometric types. In this paper, we prove that the Laurent phenomenon holds in these generalized quantum cluster algebras. We…
We define new higher-order Alexander modules $\mathcal{A}_n(C)$ and higher-order degrees $\delta_n(C)$ which are invariants of the algebraic planar curve $C$. These come from analyzing the module structure of the homology of certain…
This is a survey of a variety of equivariant (co)homology theories for operator algebras. We briefly discuss a background on equivariant theories, such as equivariant $K$-theory and equivariant cyclic homology. As the main focus, we discuss…
The Linearization Theorem for proper Lie groupoids organizes and generalizes several results for classic geometries. Despite the various approaches and recent works on the subject, the problem of understanding invariant linearization…
Generalizing deformation quantizations with separation of variables of a K\"ahler manifold $M$, we adopt Fedosov's gluing argument to construct a category $\mathsf{DQ}$, enriched over sheaves of $\mathbb{C}[[\hbar]]$-modules on $M$, as a…
It is well-known that the central extensions of the loop group of a compact, simple and 1-connected Lie group are parametrised by their level $k \in Z$. This article concerns the question how much can be said for arbitrary $k \in R$ and we…
In this paper, we study the isomorphism problem for central extensions. More precisely, in some new situations, we provide necessary and sufficient conditions for two central extensions to be isomorphic. We investigate the case when the…
After the fundamental work of Livschitz in [1; 2], various research directions emerged, among which the following stand out: (i) the study of cocycles with values in groups and semigroups beyond R, as well as the investigation of…
Geometric Quantization is a term used to describe a wide collection of techniques dating back to the 1960s in the work of Kirillov, Kostant, and Souriau, which take symplectic manifolds and produce complex vector spaces. The name comes from…
In these lectures notes I discuss the Linearization Theorem for Lie groupoids, and its relation to the various classical linearization theorems for submersions, foliations and group actions. In particular, I explain in some detail the…
This is the third and final installment of an exposition of an ACL2 formalization of finite group theory. Part I covers groups and subgroups, cosets, normal subgroups, and quotient groups. Part II extends the theory in the developmnent of…
Into this note we collect topics related to homogeneous vector bundles, elliptic adjoint orbits and so forth.
These notes give an introduction to the quantization procedure called geometric quantization. It gives a definition of the mathematical background for its understanding and introductions to classical and quantum mechanics, to differentiable…
We study a generalization of the classical correspondence between homogeneous quadratic polynomials, quadratic forms, and symmetric/alternating bilinear forms to forms in $n$ variables. The main tool is combinatorial polarization, and the…
A pre-Lie-Rinehart algebra is an algebraic generalization of the notion of a left-symmetric algebroid. We construct pre-Lie-Rinehart algebras from r-matrices through Lie algebra actions. We study cohomologies of pre-Lie-Rinehart algebras…
The purpose of this paper is to extend the cohomology and conformal derivation theories of the classical Lie conformal algebras to Lie conformal superalgebras. Firstly, we construct the semidirect product of a Lie conformal superalgebra and…