A Variety Associated to an Algebra with Involution

An Algebra Associated to a Combinatorial Geometry

1. Preliminaries. A functor from a category of combinatorial geometries, or equivalently a category of geometric lattices, to a category of commutative algebras will be described, and some properties of this functor will be investigated. In particular, a cohomology will be associated to each point of a geometry and will be derived from the associated algebra. If (G, S) is a geometry on a set S ...

An Algebra Associated with a Spin Model

To each symmetric n × n matrix W with non-zero complex entries, we associate a vector space N , consisting of certain symmetric n × n matrices. If W satisfies n ∑ x=1 Wa,x Wb,x = nδa,b (a, b = 1, . . . , n), then N becomes a commutative algebra under both ordinary matrix product and Hadamard product (entry-wise product), so that N is the Bose-Mesner algebra of some association scheme. If W sati...

An Involution Based Left Ideal in the Hecke Algebra

We show that the Hecke algebra module carried by the involutions in a Weyl group (defined by the author and Vogan) can be identified with a left ideal in the Hecke algebra. An analogous result is proved for any Coxeter group.

The Brauer-severi Variety Associated with a Central Simple Algebra: a Survey

THE BRAUER-SEVERI VARIETY ASSOCIATED WITH A CENTRAL SIMPLE ALGEBRA: A SURVEY by

— The article describes the one-to-one correspondence between central simple algebras and Brauer-Severi varieties over a field. Non-abelian group cohomology is recalled and Galois descent is worked out in detail. The classifications of central simple algebras as well as of Brauer-Severi varieties by one and the same Galois cohomology set are explained. A whole section is devoted to the discussi...