defined by the shuffle of tensors. If the product of A is commutative, then the bar differential is a derivation with respect to the shuffle product so that B(A) is still an associative and commutative differential graded algebra. Unfortunately, in algebraic topology, algebras are usually commutative only up to homotopy: a motivating example is provided by the cochain algebra of a topological s...

Recently, A.A. Kirillov introduced an interesting class of associative algebras connected with the adjoint representation of G [Ki]. In our paper, such algebras are called g-endomorphism algebras. Each g-endomorphism algebra is a module over the algebra of invariants k[g]; furthermore, it is a direct sum of modules of covariants. Hence it is a free graded finitely generated module over k[g]. Th...

Abstract The problem of finding generators the subalgebra invariants under action a group automorphisms finite-dimensional Lie algebra on its universal enveloping is reduced to homogeneous same acting symmetric tensor algebra. This process applied prove constructive Hilbert–Nagata Theorem (including degree bounds) for in nilpotent relatively free associative endowed with an induced by represent...

We explore properties of the set of d-units of a d-algebra. A property of interest in the study of d-units in d-algebras is the weak associative property. It is noted that many other d-algebras, especially BCK-algebras, are in fact weakly associative. The existence of d/BCK-algebras which are not weakly associative is demonstrated. Moreover, the notions of a d-integral domain and a left-injecti...

We prove a generalization of the polarization identity linear algebra expressing inner product complex space in terms norm, where field scalars is extended to an associative equipped with involution, and viewed as averaging operation over compact multiplicative subgroup scalars. Using this we general form Jordan-von Neumann theorem on characterizing spaces among normed spaces, when are taken al...

where μA (resp. μB) is the multiplication of A (resp. B). We deduce that the ”natural” tensor product μA⊗B = μA ⊗ μB provides A⊗ B with a Lie-admissible algebra structure. In [2] we have defined special classes of Lie-admissible algebras with relations of definition determined by an action of the subgroupsGi of the 3-degree symmetric group Σ3. We obtain quadratic operads, denoted by Gi−Ass and ...

In a previous paper the authors have attached to each Dynkin quiver an associative algebra. The definition is categorical and the algebra is used to construct desingularizations of arbitrary quiver Grassmannians. In the present paper we prove that this algebra is isomorphic to an algebra constructed by Hernandez-Leclerc defined combinatorially and used to describe certain graded Nakajima quiver...

We present a case study on how mathematicians use automated theorem provers to solve open problems in (non-associative) algebra.

In this article we work with the degenerate affine Hecke algebra Hl corresponding to the general linear group GLl over a local non-Archimedean field. This algebra was introduced by V.Drinfeld in [D], see also [L]. The complex associative algebra Hl is generated by the symmetric group algebra CSl and by the pairwise commuting elements x1 , . . . , xl with the cross relations for p = 1 , . . . , ...

Given a left module U and a right modules V over an algebra D and a bilinear form β : U × V → D, we may define an associative algebra structure on the tensor product V ⊗D U . This algebra is called a near-matrix algebra. In this paper, we shall investigate algebras filtered by near-matrix algebras in some nice way and give a unified treatment for quasi-hereditary algebras, cellular algebras, an...