Associative Algebra
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Recent papers in Associative Algebra
A new non-associative algebra for the quantization of strongly interacting fields is proposed. The full set of quantum $(\pm)$associators for the product of three operators is offered. An algorithm for the calculation of some... more
This paper is the widely extended version of the publication, appeared in Proceedings of ISSAC'2009 conference \citep*{ALM09}. We discuss more details on proofs, present new algorithms and examples. We present a general algorithm for... more
For any category of interest ℂ we define a general category of groups with operations $\mathbb{C_G}, \mathbb{C}\hookrightarrow\mathbb{C_G}$ , and a universal strict general actor USGA(A) of an object A in ℂ, which is an object of... more
An attempt is made to interpret the interactions of bosonic open strings as defining a non-cummulative, associative algebra, and to formulate the classical non-linear field theory of such strings in the language of non-commulative... more
In this survey, we first present basic facts on A-infinity algebras and modules including their use in describing triangulated categories. Then we describe the Quillen model approach to A-infinity structures following K. Lefevre's thesis.... more
In present paper we develop the deformation theory of operads and algebras over operads. Free resolutions (constructed via Boardman-Vogt approach) are used in order to describe formal moduli spaces of deformations. We apply the general... more
We call a finite-dimensional complex Lie algebra $\mathfrak{g}$ strongly rigid if its universal enveloping algebra $\Ug$ is rigid as an associative algebra, i.e. every formal associative deformation is equivalent to the trivial... more
Nagata gave a fundamental sucient condition on group actions on nitely generated commutative algebras for nite generation of the subalge- bra of invariants. In this paper we consider groups acting on noncommutative algebras over a eld of... more
This paper is the widely extended version of the publication, appeared in Proceedings of IS-SAC'2009 conference (Andres, Levandovskyy, and Martın-Morales, 2009). We discuss more de-tails on proofs, present new algorithms and... more
In this paper we present a complete classification (isomorphism classes with some isomorphism invariants) of complex associative algebras up to dimension five (including both cases: unitary and non-unitary). In some symbolic computations... more
Using these nonstandard objects as a guide, we follow the approach of Adsul, Sohoni, and Subrahmanyam to construct, in the case dim(V) = dim(W) =2, a representation \check{X}_\nu of the nonstandard quantum group that specializes to... more
We discuss the category $\cal I$ of level zero integrable representations of loop algebras and their generalizations. The category is not semisimple and so one is interested in its homological properties. We begin by looking at some... more
The purpose of this paper is to introduce Hom-alternative algebras and Hom-Jordan algebras. We discuss some of their properties and provide construction procedures using ordinary alternative algebras or Jordan algebras. Also, we show that... more
Given an associative algebra $A$, and the category, $\cC$, of its finite dimensional modules, additional structures on the algebra $A$ induce corresponding ones on the category $\cC$. Thus, the structure of a rigid quasi-tensor (braided... more
We consider associative algebras L over a field provided with a direct sum decomposition of a two-sided ideal M and a sub-algebra A - examples are provided by trivial extensions or triangular type matrix algebras. In this relative and... more
A well-known conjecture says that every one-relator group is coherent. We state and partly prove an analogous statement for graded associative algebras. In particular, we show that every Gorenstein algebra $A$ of global dimension 2 is... more
The idea of categorification is to replace "simpler" objects with "more complicated" ones. The aim is to get some new information in terms of some extra structure of the complicated objects. In particular, it can be used in representation... more
Given a Hopf algebra A, there exist various cohomology theories for the category of Hopf bimodules over A, introduced by M. Gerstenhaber and S.D. Schack, and by C. Ospel. We prove, when A is finite dimensional, that they are equal to the... more
The theory of associative algebras of quotients has a rich history and is still an active research area. In the recent paper (24), the author iniciated the study of algebras of quotients in the Lie setting and built a maximal algebra of... more
A cyclic cohomology theory adapted to Hopf algebras has been introduced recently by Connes and Moscovici. In this paper, we consider this object in the homological framework, in the spirit of Loday-Quillen and Karoubi's work on the cyclic... more
As is well-known, the real quaternion division algebra ℍ is algebraically isomorphic to a 4-by-4 real matrix algebra. But the real division octonion algebra can not be algebraically isomorphic to any matrix algebras over the real number... more