Generic algebras

Generic modules over artin algebras

Generic modules have been introduced by Crawley-Boevey in order to provide a better understanding of nite dimensional algebras of tame representation type. In fact he has shown that the generic modules correspond to the one-parameter families of indecomposable nite dimensional modules over a tame algebra 5]. The Second Brauer-Thrall Conjecture provides another reason to study generic modules be...

Generic Algebras with Involution Of

6 Generic Hecke Algebras for Monomial Groups

In this paper we define a two-variable, generic Hecke algebra, H, for each complex reflection group G(b, 1, n). The algebra H specializes to the group algebra of G(b, 1, n) and also to an endomorphism algebra of a representation of GLn(Fq) induced from a solvable subgroup. We construct Kazhdan-Lusztig “R-polynomials” for H and show that they may be used to define a partial order on G(b, 1, n). ...

Generic Algebras: Rational Parametrization and Normal Forms

For every algebraically closed field k of characteristic different from 2, we prove the following: (1) Generic finite dimensional (not necessarily associative) kalgebras of a fixed dimension, considered up to isomorphism, are parametrized by the values of a tuple of algebraically independent over k rational functions in the structure constants. (2) There exists an “algebraic normal form”, to wh...

Enriched Generic Algebras of Fuzzy Relations

The paper presents an overview of a computation friendly calculus of fuzzy relations. It is presented within the framework of an enriched generic algebra of relations that we have been developing since 1979. It is enriched with BK-non-associative products of relations of three kinds: triangle subproduct C, superproduct B and the square product . The BK-products have been useful in concise formu...