Related papers: On Deformations of Associative Algebras
In this paper, we initiate the study of endomorphisms and modular theory of the graph C*-algebras $\O_{\theta}$of a 2-graph $\Fth$ on a single vertex. We prove that there is a semigroup isomorphism between unital endomorphisms of…
We give a description of cyclic cohomology and its pairing with K-groups for 2-cocycle deformation of algebras graded over discrete groups. The proof relies on a realization of monodromy for the Gauss-Manin connection on periodic cyclic…
Let $R=\oplus_{\Gamma\in\Gamma}R_{\gamma}$ be a $\Gamma$-graded $K$-algebra over a field $K$, where $\Gamma$ is a totally ordered semigroup, and let $I$ be an ideal of $R$. Considering the $\Gamma$-grading filtration $FR$ of $R$ and the…
We calculate the first Hochschild cohomology group of quantum matrices, the quantum general linear group and the quantum special linear group in the generic case when the deformation parameter is not a root of unity. As a corollary, we…
A first goal of this paper is to precisely relate the homotopy theories of bialgebras and $E_2$-algebras. For this, we construct a conservative and fully faithful $\infty$-functor from pointed conilpotent homotopy bialgebras to augmented…
The dimension algebra of graded groups is introduced. With the help of known geometric results of extension theory that algebra induces all known results of the cohomological dimension theory. Elements of the algebra are equivalence classes…
Let $A=A(\alpha, \beta)$ be a graded down-up algebra with weights $(\mathrm{deg}\, x, \mathrm{deg}\, y)=(n,m)$ and $\beta \neq 0$, and $\nabla A$ its Beilinson algebra. Such an algebra $A$ is a 3-dimensional cubic AS-regular algebra by…
The first (associative) Weyl algebra is formally rigid in the classical sense. In this paper, we show that it can however be formally deformed in a nontrivial way when considered as a so-called hom-associative algebra, and that this…
The aim of this paper is to provide a cohomology of $n$-Hom-Lie color algebras governing one parameter formal deformations. Then, we study formal deformations of a $n$-Hom-Lie color algebra and introduce the notion of Nijenhuis operator on…
Let H be a graded Hecke algebra with complex deformation parameters and Weyl group W. We show that the Hochschild, cyclic and periodic cyclic homologies of H are all independent of the parameters, and compute them explicitly. We use this to…
A procedure for constructing bivariant theories by means of Grothendieck duality is developed. This produces, in particular, a bivariant theory of Hochschild (co)homology on the category of schemes that are flat, separated and essentially…
We give a new computation of Hochschild (co)homology of the exterior algebra, together with algebraic structures, by direct comparison with the symmetric algebra. The Hochschild cohomology is determined to be essentially the algebra of…
We introduce a class of densely defined, unbounded, 2-Hochschild cocycles ([PT]) on finite von Neumann algebras $M$. Our cocycles admit a coboundary, determined by an unbounded operator on the standard Hilbert space associated to the von…
One way to understand the deformation theory of a tensor category $M$ is through its Davydov-Yetter cohomology $H_{DY}^{\ast}(M)$ which in degree 3 and 4 is known to control respectively first order deformations of the associativity…
A hom-associative algebra is an algebra whose associativity is twisted by an algebra homomorphism. It was previously shown by the author that the Hochschild cohomology of a hom-associative algebra $A$ carries a Gerstenhaber structure. In…
We study formal deformations of a crossed product $S(V)#_f G$, of a polynomial algebra with a group, induced from a universal deformation formula introduced by Witherspoon. These deformations arise from braided actions of Hopf algebras…
Given a coalgebra C over a cooperad, and an algebra A over an operad, it is often possible to define a natural homotopy Lie algebra structure on hom(C,A), the space of linear maps between them, called the convolution algebra of C and A. In…
We study functors underlying derived Hochschild cohomology, also called Shukla cohomology, of a commutative algebra S essentially of finite type and of finite flat dimension over a commutative noetherian ring K. We construct a complex of…
The main purpose of this paper is to study restricted formal deformations of restricted Lie-Rinehart algebras in positive characteristic $p$. For $p>2$, we discuss the deformation theory and show that deformations are controlled by the…
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…