The purpose of this article is to determine representation type for all of the Hecke algebras of classical type. To do this, we combine methods from our previous work, which is used to obtain information on their Gabriel quivers, and recent advances in the theory of finite dimensional algebras.

Let k be a field. We prove that any polynomial ring over k is a Kadison algebra if and only if k is infinite. Moreover, we present some new examples of Kadison algebras and examples of algebras which are not Kadison algebras.

The study of the representation theory of the symmetric groups (and, more recently, the Iwahori–Hecke algebras of type A) has always been inextricably linked with the combinatorics of partitions. More recently, the complex reflection group of type G(r, 1, n) and its Hecke algebras (the Ariki–Koike algebras or cyclotomic Hecke algebras) have been studied, and it is clear that there is a similar ...

Given a simple atomic relation algebra A and a finite n ≥ 3, we construct effectively an atomic n-dimensional polyadic equality-type algebra P such that for any subsignature L of the signature of P that contains the boolean operations and cylindrifications, the L-reduct of P is completely representable if and only if A is completely representable. If A is finite then so is P. It follows that th...

Let's read! We will often find out this sentence everywhere. When still being a kid, mom used to order us to always read, so did the teacher. Some books are fully read in a week and we need the obligation to support reading. What about now? Do you still love reading? Is reading only for you who have obligation? Absolutely not! We here offer you a new book enPDFd fork algebras in algebra logic a...

We survey three recent developments in algebraic combinatorics. The first is the theory of cluster algebras and the Laurent phenomenon of Sergey Fomin and Andrei Zelevinsky. The second is the construction of toric Schur functions and their application to computing three-point Gromov-Witten invariants, by Alexander Postnikov. The third development is the construction of intersection cohomology f...

We continue a previous study on Γ-vertex algebras and their quasimodules. In this paper we refine certain known results and we prove that for any Z-graded vertex algebra V and a positive integer N , the category of V -modules is naturally isomorphic to the category of quasimodules of a certain type for V ⊗N . We also study certain generalizations of twisted affine Lie algebras and we relate suc...

In this paper, we deal to obtain some new complexity results for solving semidefinite optimization (SDO) problem by interior-point methods (IPMs). We define a new proximity function for the SDO by a new kernel function. Furthermore we formulate an algorithm for a primal dual interior-point method (IPM) for the SDO by using the proximity function and give its complexity analysis, and then we sho...

The involutions in this paper are algebra anti-automorphisms of period two. Involutions on endomorphism algebras of finite-dimensional vector spaces are adjoint to symmetric or skew-symmetric bilinear forms, or to hermitian forms. Analogues of the classical invariants of quadratic forms (discriminant, Clifford algebra, signature) have been defined for arbitrary central simple algebras with invo...