Let k be an algebraically closed field of characteristic p. We give the complete classification pointed Hopf algebras over dimension p2q for a prime number q. The result shows that there are finitely many isomorphism classes, including 10 classes not generated by group-like elements and skew-primitive elements. In particular, new examples finite-dimensional algebras.

Let S be a semigroup and K be a field. A K-space K[S], with basis S and with multiplication extending, in a natural way, the operation on S, is called a semigroup algebra. It remains an open problem to characterize semigroup algebras that are a prime Noetherian maximal order. In this thesis, we give an answer to the problem for a large class of cancellative semigroups and we illustrate these re...

In this paper, applying the concept of generalized A-valued norm on a right $H^*$-module and also the notion of ϕ-homomorphism of Finsler modules over $C^*$-algebras we first improve the definition of the Finsler module over $H^*$-algebra and then define ϕ-morphism of Finsler modules over $H^*$-algebras. Finally we present some results concerning these new ones.

Aside from intrinsic interest there are three (related) reasons for studying the unitary representations of £-adic division algebras. (1) They provide heuristics for more difficult (e.g., noncompact) £-adic groups. (2) They would be basic building blocks in a theory of representations of reductive algebraic £-adic groups based on the philosophy of cusp forms. (3) There seem to be deep relations...

Abstract The classical Gleason-Kahane-Żelazko Theorem states that a linear functional on complex Banach algebra not vanishing units, and such $$\Lambda (\textbf{1})=1$$ Λ ( 1 ) = , is multiplicative, is, (ab)=\Lambda (a...

Let G be a finite group that acts on an abelian monoid A. If φ : A → G is a map so that φ(aφ(a)(b)) = φ(a)φ(b), for all a, b ∈ A, then the submonoid S = {(a, φ(a)) | a ∈ A} of the associated semidirect product A⋊G is said to be a monoid of IG-type. If A is a finitely generated free abelian monoid of rank n and G is a subgroup of the symmetric group Sym n of degree n, then these monoids first ap...