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2011 Group algebra extensions of depth one
Robert Boltje, Burkhard Külshammer
Algebra Number Theory 5(1): 63-73 (2011). DOI: 10.2140/ant.2011.5.63

Abstract

A ring extension AB is said to have depth one if B is isomorphic to a direct summand of An as an (A,A)-bimodule, for some positive integer n. We prove group-theoretic characterizations of this property in the case kHkG, where H is a subgroup of a finite group G and k is a field. We determine when the source algebra of a block of kG with defect group P is a depth-one extension of kP.

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Robert Boltje. Burkhard Külshammer. "Group algebra extensions of depth one." Algebra Number Theory 5 (1) 63 - 73, 2011. https://doi.org/10.2140/ant.2011.5.63

Information

Received: 15 January 2010; Revised: 22 April 2010; Accepted: 6 June 2010; Published: 2011
First available in Project Euclid: 20 December 2017

zbMATH: 1236.20001
MathSciNet: MR2833785
Digital Object Identifier: 10.2140/ant.2011.5.63

Subjects:
Primary: 20C05
Secondary: 16D20 , 16D90 , 19A22 , 20C20

Keywords: $p$-hypoelementary group , centrally projective ring extension , depth-one ring extension , depth-two ring extension , nilpotent block , source algebra , symmetric Frobenius extension , trivial source module

Rights: Copyright © 2011 Mathematical Sciences Publishers

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