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We show that there is an action of the symmetric group on the Hochschild cochain complex of a twisted group algebra with coefficients in a bimodule. This allows us to define the symmetric Hochschild cohomology of twisted group algebras,…
We study twisted modules for (weak) quantum vertex algebras and we give a conceptual construction of (weak) quantum vertex algebras and their twisted modules. As an application we construct and classify irreducible twisted modules for a…
We study \'etale descent of derivations of algebras with values in a module. The algebras under consideration are twisted forms of algebras over rings, and apply to all classes of algebras, notably associative and Lie algebras, such as the…
Twisted current algebras are fixed point subalgebras of current algebras under a finite group action. Special cases include equivariant map algebras and twisted forms of current algebras. Their finite-dimensional simple modules fall into…
Twisted loop algebras of the second kind are infinite-dimensional Lie algebras that are constructed from a semisimple Lie algebra and an automorphism on it of order at most $2$. They are examples of equivariant map algebras. The…
We decompose the full and reduced C*-algebras of an extension of a groupoid by the circle into a direct sum of twisted groupoid C*-algebras.
We produce a long exact sequence whose terms are unit groups of associative algebras that behave as inner automorphisms of a given tensor. Our sequence generalizes known sequences for associative and non-associative algebras. In a manner…
We introduce a simple procedure to integrate differential forms with arbitrary holomorphic poles on Riemann surfaces. It gives rise to an intrinsic regularization of such singular integrals in terms of the underlying conformal geometry.…
We give a general treatment of the master equation in homotopy algebras and describe the operads and formal differential geometric objects governing the corresponding algebraic structures. We show that the notion of Maurer-Cartan twisting…
We introduce magnetic twisted actions of X=R^n on general abelian C*-algebras and study the associated twisted crossed product and pseudodifferential algebras in the framework of strict deformation quantization.
We define vertex cover algebras for weighted simplicial multicomplexes and prove basics properties of them. Also, we describe these algebras for multicomplexes which have only one maximal facet and we prove that they are finitely generated.
The algebraic study of special integral operators led to the notions of Rota-Baxter operators and shuffle products which have found broad applications. This paper carries out an algebraic study of general integral operators and equations,…
We study a twisted generalization of Novikov algebras, called Hom-Novikov algebras, in which the two defining identities are twisted by a linear map. It is shown that Hom-Novikov algebras can be obtained from Novikov algebras by twisting…
With any involutive anti-algebra and coalgebra automorphism of a quasitriangular bialgebra we associate a reflection equation algebra. A Hopf algebraic treatment of the reflection equation of this type and its universal solution is given.…
Automorphisms of structural matrix algebras in block upper triangular form has been studied recently in \cite{Akkurt E-M Barker 2}, and this work is a follow-up paper of that study. The aim of this paper is to explain the topic in a much…
In this paper we introduce the notion of twisted symplectic reflection algebras and describe the category of representations of such an algebra associated to a non-faithful G-action in terms of those for faithful actions of G.
A loop whose inner mappings are automorphisms is an \emph{automorphic loop} (or \emph{A-loop}). We characterize commutative (A-)loops with middle nucleus of index 2 and solve the isomorphism problem. Using this characterization and certain…
We continue with [LY] to construct and classify graded simple twisted modules for the $\N$-graded vertex algebras constructed by Gorbounov, Malikov and Schechtman from vertex algebroids. Meanwhile we determine the full automorphism groups…
We present a prescription for choosing orthogonal bases of differential $n$-forms belonging to quadratic twisted period integrals, with respect to the intersection number inner product. To evaluate these inner products, we additionally…
We establish closed-form expansions for the universal edge elimination polynomial of paths and cycles and their generating functions. This includes closed-form expansions for the bivariate matching polynomial, the bivariate chromatic…