Let $G$ be a split connected reductive group over $\mathbb{Z}$. $F$ non-archimedean local field. With $K_m: = Ker(G(\mathfrak{O}_F) \rightarrow G(\mathfrak{O}_F/\mathfrak{p}_F^m))$, Kazhdan proved that for field $F'$sufficiently close to $F$, the Hecke algebras $\mathcal{H}(G(F),K_m)$ and $\mathcal{H}(G(F'),K_m')$ are isomorphic, where $K_m'$ denotes corresponding object $F'$. In this article, ...

(abstract) The algebra of all binary relations on a given set is the most important example of a relation algebra (cf. [3]). In this note we will examine the possible isomorphisms within some subclasses of a closely related class (cf. [1] 5.3.2); A is a relation set algebra with base U if its Boolean reduct is a field of sets with unit element 2 U , its universe A contains the identity relation...

An isomorphism is established between the plethystic Hopf algebra Pleth(Super[L]) and the algebra of vector symmetric functions. The Hall inner product of symmetric function theory is extended to the Hopf algebra Pleth(Super[L]).

In this work, the Z3-graded differential geometry of the quantum plane is constructed. The corresponding quantum Lie algebra and its Hopf algebra structure are obtained. The dual algebra, i.e. universal enveloping algebra of the quantum plane is explicitly constructed and an isomorphism between the quantum Lie algebra and the dual algebra is given. E-mail: [email protected]

The concept of abstract algebra on intuitionistic fuzzy sets were introduced and some basic theorems proved by authors in 2017. In this study, homomorphism between algebras is defined, function examined then congruence relations are defined algebra. First third isomorphism introduced.

In this paper, we present an isomorphism between the ring of general polynomials over a division algebra D with center F and the group ring of the free monoid with [D : F ] variables over D. Using this isomorphism, we define the characteristic polynomial of any matrix over any division algebra, i.e., a general polynomial with one variable over the algebra whose roots are precisely the left eige...

Let S be a degree six del Pezzo surface over an arbitrary field F . Motivated by the first author’s classification of all such S up to isomorphism [3] in terms of a separable F -algebra B×Q×F , and by his K-theory isomorphism Kn(S) ∼= Kn(B × Q × F ) for n ≥ 0, we prove an equivalence of derived categories D (cohS) ≡ D(modA) where A is an explicitly given finite dimensional F -algebra whose semi...

We build, using the notion of zinbiel algebra, some commutative subalgebras C_{u,v} inside an algebra formal iterated integrals. There is a quotient map from this integrals to motivic multiple zeta values. Restricting gives morphism graded algebras with same dimension. This conjectured be generically isomorphism. When u+v = 0, image instead sub-algebra

We consider algebras over a field k of characteristic zero. The article is concerned with the isomorphism of graded vectorspaces H(gl(A)) ∼ → ∧(HC(A)[−1]) between the Lie algebra homology of matrices and the free graded commutative algebra on the cyclic homology of the k-algebra A, shifted down one degree. For unital algebras this isomorphism is a classical result obtained by Loday and Quillen ...

We study the relationship between algebraic structures and their inverse semigroups of partial automorphisms. We consider a variety of classes of natural structures including equivalence structures, orderings, Boolean algebras, and relatively complemented distributive lattices. For certain subsemigroups of these inverse semigroups, isomorphism (elementary equivalence) of the subsemigroups yield...