In this paper, some properties of the dual B-homomorphism are provided, along with natural and fundamental theorem B-homomorphisms for B-algebras. The first third isomorphism theorems B algebra also presented in paper.

In this paper we are interested in the order structure induced by the relations ’before’ and ’meets’ of Allen’s interval algebra. We provide an abstract definition of this kind of order structure called an interval order. We prove that every interval order is isomorphic to the corresponding order on a set of finite intervals over a linear order without endpoints. As a consequence of this charac...

Motivated by recent results of A. Klyachko, we construct a probability preserving, isometric isomorphism from the Banach algebra Mb(SL(d,C)‖SU(d)) of all SU(d)-biinvariant bounded signed measures on SL(d,C) to some Banach subalgebra of the Banach algebra of all bounded signed measures on the Euclidean space of all Hermitian d × d-matrices with trace 0. This isomorphism leads to strong limit the...

In this paper, a semigroup algebra consisting of polynomial expressions with coefficients in field F and exponents an additive submonoid M Q≥0 is called Puiseux denoted by F[M]. Here we study the atomic structure algebras. To begin with, answer isomorphism problem for class algebras, that is, show if two algebras F[M1] F[M2] are isomorphic, then monoids M1 M2 must be isomorphic. Then construct ...

To any finite group G SL2ðCÞ and each element t in the center of the group algebra of G, we associate a category, CohðP G;t ;PÞ: It is defined as a suitable quotient of the category of graded modules over (a graded version of) the deformed preprojective algebra introduced by Crawley-Boevey and Holland. The category CohðP G;t ;PÞ should be thought of as the category of coherent sheaves on a ‘non...

We introduce the spin Hecke algebra, which is a q-deformation of the spin symmetric group algebra, and its affine generalization. We establish an algebra isomorphism which relates our spin (affine) Hecke algebras to the (affine) Hecke-Clifford algebras of Olshanski and Jones-Nazarov. Relation between the spin (affine) Hecke algebra and a nonstandard presentation of the usual (affine) Hecke alge...

It is well known that the Clifford algebra Cl p,q associated to a nondegenerate quadratic form on R n (n = p + q) is isomorphic to a matrix algebra K(m) or direct sum K(m) ⊕ K(m) of matrix algebras, where K = R, C, H. On the other hand, there are no explicit expressions for these isomorphisms in literature. In this work, we give a method for the explicit construction of these isomorphisms. Let ...

The Kontsevich integral of a knot K lies in an algebra of diagrams Ac(S ). This algebra is (up to completion) a symmetric algebra of a graded module P , where P is the set of primitive elements of Ac(S ). The elements of P are represented by S-diagrams K such that the complement of the circle in K is connected and non empty. On the other hand there is an isomorphism from ⊕Bn to Ac(S ), where Bn...

We construct an isomorphism between the partially ordered set of tilting modules for Auslander algebra K[x]/(xn) and interval rational permutation braids in braid group on n strands. Hence, there are only finitely many modules.

By Tits’ deformation argument, a generic Iwahori–Hecke algebra H associated to a finite Coxeter group W is abstractly isomorphic to the group algebra of W . Lusztig has shown how one can construct an explicit isomorphism, provided that the Kazhdan–Lusztig basis of H satisfies certain deep properties. If W is crystallographic and H is a one-parameter algebra, then these properties are known to h...