Odd H-depth and H-separable extensions

• Autorzy: Lars Kadison
• Języki publikacji: EN

Abstrakty

EN

Let C n(A,B) be the relative Hochschild bar resolution groups of a subring B ⊆ A. The subring pair has right depth 2n if C n+1(A,B) is isomorphic to a direct summand of a multiple of C n(A,B) as A-B-bimodules; depth 2n + 1 if the same condition holds only as B-B-bimodules. It is then natural to ask what is defined if this same condition should hold as A-A-bimodules, the so-called H-depth 2n − 1 condition. In particular, the H-depth 1 condition coincides with A being an H-separable extension of B. In this paper the H-depth of semisimple subalgebra pairs is derived from the transpose inclusion matrix, and for QF extensions it is derived from the odd depth of the endomorphism ring extension. For general extensions characterizations of H-depth are possible using the H-equivalence generalization of Morita theory.

Słowa kluczowe

EN

Subring depth; H-separable; Frobenius extension; Complex semisimple algebra

Kategorie tematyczne

• 16D20: Bimodules
• 16G60: Representation type (finite, tame, wild, etc.)
• 16S50: Endomorphism rings; matrix rings

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 3
• Strony: 958-968

Daty

wydano

2012-06-01

online

2012-03-24

Twórcy

autor

Lars Kadison

• Faculdade de Ciências da Universidade do Porto

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-012-0013-y