Related papers: Tensor calculus and deformation theory on on a loc…

We generalize the classical construction principles of infinite-dimensional real (and complex) Lie groups to the case of Lie groups over non-discrete topological fields. In particular, we discuss linear Lie groups, mapping groups, test…

We describe a q-deformation of the Lorentz group in terms of a q-deformation of the van der Waerden spinor algebra.

We start studying chiral algebras (as defined by A. Beilinson and V. Drinfeld) from the point of view of deformation theory. First, we define the notion of deformation of a chiral algebra on a smooth curve $X$ over a bundle of local…

The notion of a tensor captures three great ideas: equivariance, multilinearity, separability. But trying to be three things at once makes the notion difficult to understand. We will explain tensors in an accessible and elementary way…

Algebraic deformations of modules over a ring are considered. The resulting theory closely resembles Gerstenhaber's deformation theory of associative algebras.

We briefly summarize our systematic construction procedure of q-deforming maps for Lie group covariant Weyl or Clifford algebras.

Starting from the classical r-matrix of the non-standard (or Jordanian) quantum deformation of the sl(2,R) algebra, new triangular quantum deformations for the real Lie algebras so(2,2), so(3,1) and iso(2,1) are simultaneously constructed…

In this paper we study multilinear morphisms between commutative group schemes and the associated tensor constructions. We will also do some explicit calculations and give examples that show that this theory behaves in a way that one would…

We develop a theory of descent and forms of tensor categories over arbitrary fields. We describe the general scheme of classification of such forms using algebraic and homotopical language, and give examples of explicit classification of…

In the literature various notions of nonlocal curvature can be found. Here we propose a notion of nonlocal curvature tensor. This we do by generalizing an appropriate representation of the classical curvature tensor and by exploiting some…

We develop the Lie theory of Lie-admissible algebras whose product is enriched with higher operations modeled on directed graphs with a view to apply it to the deformation theories controlled by this kind of Lie algebras. We produce…

We construct a one parameter deformation of the group of $2\times 2$ upper triangular matrices with determinant 1 using the twisting construction. An interesting feature of this new example of a locally compact quantum group is that the…

A quantum deformation of 3-dimensional lattice gauge theory is defined by applying the Reshetikhin-Turaev functor to a Heegaard diagram associated to a given cell complex. In the root-of-unity case, the construction is carried out with a…

We provide a brief overview of tensor models and group field theories, focusing on their main common features. Both frameworks arose in the context of quantum gravity research, and can be understood as higher-dimensional generalizations of…

First three sections of this overview paper cover classical topics of deformation theory of associative algebras and necessary background material. We then analyze algebraic structures of the Hochschild cohomology and describe the relation…

In this note, we use give some algebraic applications of a previous result by the author which compares the deformations parameterized by the Maurer-Cartan elements of a differential graded Lie algebra, and a differential graded Lie…

A consistent classical mechanics formulation is presented in such a way that, under quantization, it gives a noncommutative quantum theory with interesting new features. The Dirac formalism for constrained Hamiltonian systems is strongly…

We show how one can construct a differential calculus over an algebra where position variables x and momentum variables p have be defined. As the simplest example we consider the one-dimensional q-deformed Heisenberg algebra. This algebra…

We develop the deformation-obstruction calculus for morphisms of complexes with a fixed lift of the codomain, to derived categories of flat nilpotent deformations of abelian categories. As an application, we give an alternative proof that…

In past few decades, tensor algebra also known as multi-linear algebra has been developed and customized as a tool to be used for various engineering applications. In particular, with the help of a special form of tensor contracted product,…