Degree Of Generation Research Articles

The representations and generic degrees of the Hecke algeba of type H4.

Article The representations and generic degrees of the Hecke algeba of type H4. was published on January 1, 1982 in the journal Journal für die reine und angewandte Mathematik (volume 1982, issue 336).

Finitely generated codings and the degrees r.e. in a degree 𝑑

We introduce finitely generated (partial) lattices which can be used to code an arbitrary set D D . Results of Lerman, Shore and Soare are used to embed these lattices in the degrees r.e. in D D . Thus if the degrees r.e. in and above d {\mathbf {d}} are isomorphic to those r.e. in and above c {\mathbf {c}} , d {\mathbf {d}} and c {\mathbf {c}} are of the same arithmetic degree. Similar applications are given to generic degrees and general homogeneity questions.

The generic degrees of the irreducible characters of e8

The generic degrees of the irreducible characters of e8

Noncommutative Jordan division algebras

The structure theory for noncommutative Jordan algebras with chain conditions leads to the following simple algebras: (I) division algebras, (II) forms of nodal algebras, (III) algebras of generic degree two, (IV) commutative Jordan matrix algebras, (V) quasi-associative algebras. The chain condition is always satisfied in a division algebra, hence does not serve as a finiteness restriction. Consequently, the general structure of noncommutative Jordan division algebras, even commutative Jordan division algebras, is unknown. In this paper we will classify those non-commutative Jordan division algebras which are forms of algebras of types (II)-(V); this includes in particular all the finite-dimensional ones.