We establish a 3-manifold invariant for each finite-dimensional, involutory Hopf algebra. If the Hopf algebra is the group algebra of a group G, the invariant counts homomorphisms from the fundamental group of the manifold to G. The invariant can be viewed as a state model on a Heegaard diagram or a triangulation of the manifold. The computation of the invariant involves tensor products and con...

Let X,Y be locally compact Hausdorff spaces and M,N be Banach algebras. Let θ : C0(X,M) → C0(Y,N ) be a zero-product preserving bounded linear map with dense range. We show that θ is given by a continuous field of algebra homomorphisms from M into N if N is irreducible. As corollaries, such a surjective θ arises from an algebra homomorphism, provided thatM is a W*-algebra and N is a semi-simple...

We exhibit an adjunction between a category of abstract algebras partial functions and set quotients. The are those atomic representable as collection closed under relative complement domain restriction; the morphisms complete homomorphisms. This generalises discrete Boolean sets. define compatible completion algebra, show that monad induced by our yields any algebra. As corollary, restricts to...

We show that there is an action of the symmetric group on Hochschild cochain complex a twisted algebra with coefficients in bimodule. This allows us to define cohomology algebras, similarly th construction due Staic. give explicit embeddings and connecting homomorphisms between spaces algebras.

Here G is considered as an algebraic group defined over F . The Lie algebra g may be identified with Mn(F ), with Lie bracket [X,Y ] = XY − Y X . The group T is isomorphic to the algebraic torus Gm, T (F ) is isomorphic to (F), and the Lie algebra t is isomorphic to F. The character group X(T ) is the lattice of algebraic homomorphisms T → Gm, the cocharacter group that of algebraic homomorphis...

Let X be a locally finite regular affine building with root system R. There is a commutative algebra A spanned by averaging operators A λ , λ ∈ P + , acting on the space of all functions f : V P → C, where V P is in most cases the set of all special vertices of X , and P + is a set of dominant coweights of R. This algebra is studied in [6] and [7] for˜An buildings, and the general case is treat...

The concept of the direct product finite family \(\textit{B}\)-algebras is introduced by Lingcong and Endam [J. A. V. Lingcong, J. C. Endam, Int. Algebra, \(\textbf{10}\) (2016), 33--40]. In this paper, we introduce infinite BCC-algebras prove that it a dual (dBCC-algebras), call external dBCC-algebra induced BCC-algebras, which general in sense Endam. We find result special subsets BCC-algebra...