Irreducible complex skew-Berger algebras

Berger algebras, weak-Berger algebras and Lorentzian holonomy

Skew shape representations are irreducible

Abstract. In this paper all of the classical constructions of A. Young are generalized to affine Hecke algebras of type A. It is proved that the calibrated irreducible representations of the affine Hecke algebra are indexed by placed skew shapes and that these representations can be constructed explicitly with a generalization of Young’s seminormal construction of the irreducible representation...

1 5 Ja n 20 07 SKEW HOPF ALGEBRAS AND IRREDUCIBLE EXTENSIONS

To a depth two extension A|B, we associate standard dual bialge-broids S := End B A B and T := (A ⊗ B A) B over the centralizer R = C A (B). In a common setup where R is a subalgebra of B, two nondegenerate pairings of S and T will define an anti-automorphism τ of the algebra S. Making use of a two-sided depth two structure, we show that τ is an antipode and S is a Hopf algebroid of a type we c...

Free skew Boolean algebras

Subdirectly irreducible separable dynamic algebras

A characterization of the subdirectly irreducible separable dynamic algebras is presented. The notions developed for this study were also suitable to describe the previously found class of the simple separable dynamic algebras.