相关论文: Basic cohomology of associative algebras
The purpose of this paper is to study the structure and the algebraic varieties of Hom-associative algebras. We give characterize multiplicative simple Hom-associative algebras and show some examples deforming the $2\times 2$-matrix algebra…
The main purpose of this paper is to provide a full cohomology of a Hom-pre-Lie algebra with coefficients in a given representation. This new type of cohomology exploit strongly the Hom-type structure and fits perfectly with simultaneous…
We give a conceptual explanation of universal deformation formulas for unital associative algebras and prove some results on the structure of their moduli spaces. We then generalize universal deformation formulas to other types of algebras…
A correspondence between a monogenic function in an arbitrary finite-dimensional commutative associative algebra and a finite set of monogenic functions in a special commutative associative algebra is established.
A way to characterize the space of leaves of a foliation in terms of connections is proposed. A particular example of vertex algebra cohomology of codimension one foliations on complex curves is considered.
We classify unital associative conformal algebras of linear growth and provide new examples of such.
In this paper, we introduce the notion of BiHom-Lie conformal superalgebras. We develop its representation theory and define the cohomology group with coefficients in a module. Finally, we introduce conformal derivations of BiHom-Lie…
The paper studies the structure of restricted hom-Lie algebras. More specifically speaking, we first give the equivalent definition of restricted hom-Lie algebras. Second, we obtain some properties of $p$-mappings and restrictable hom-Lie…
We introduce many new generalizations of Poisson algebras which can be constructed inside the associative algebra of linear transformations over a vector space.
We determine the product structure on Hochschild cohomology of commutative algebras in low degrees, obtaining the answer in all degrees for complete intersection algebras. As applications, we consider cyclic extension algebras as well as…
The purpose of this paper is to provide a cohomology of $n$-Hom-Leibniz algebras. Moreover, we study some higher operations on cohomology spaces and deformations.
We compute the Hochschild cohomology and homology of a class of quantum exterior algebras, with coefficients in twisted bimodules. As a result we obtain several interesting examples of the homological behavior of these algebras.
We present alternative postulates for Euclidean geometry whose merit is that they lead to a new class of invariants and associated geometries for real finite-dimensional unital associative algebras.
We define for an associative algebra an $A_{\infty}$ category whose objects are automorphisms of this algebra. This construction has some resemblance with Fukaya'a categories related to Floer cohomology.
We compute the second (and the first) cohomology groups of $^*$-algebras associated to the universal quantum unitary groups of not neccesarily Kac type, extending our earlier results for the free unitary group $U_d^+$. The extended setup…
We define cyclic cohomology of corings over not necessarily commutative algebras. We observe that the key fact which allows us to define this complex is that enveloping algebra of an algebra is a para Hopf algebroid. This observation…
In this paper, we first recall the notion of (noncommutative) Poisson conformal algebras and describe some constructions of them. Then we study the formal distribution (noncommutative) Poisson algebras and coefficient (noncommutative)…
Both the basic cohomology groups and the reduced cohomology groups of the Schr\"odinger-Virasoro conformal algebra with trivial coefficients are completely determined.
In this paper, we give a new series of coboundary operators of Hom-Lie algebras. And prove that cohomology groups with respect to coboundary operators are isomorphic. Then, we revisit representations of Hom-Lie algebras, and generalize the…
In this note we compute the cohomology of the elliptic tangent bundle, a Lie algebroid used to describe singular symplectic forms arising from generalized complex geometry.