A Course in Homological Algebra

“…The three-lemma [49] and the open mapping theorem imply that T must be an isomorphism. An exact sequence is said to split if it is equivalent to the trivial sequence 0 → Y → Y ⊕ Z → Z → 0; equivalently, Y is complemented in X (the injection Y → X admits a left inverse) or, equivalently, the quotient map X → X/Y admits a right inverse.…”

Section: Exact Sequences Of Quasi-banach Spacesmentioning

confidence: 99%

Banach space techniques underpinning a theory for nearly additive mappings

Sánchez

Castillo

2002

Dissertationes Math.

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Ulam's stability problem for additive maps and the theory of extensions of Banach spaces have remained so far unaware of each other. To support this assertion it is enough to peruse the survey articles [36,52] In fact, both worlds constitute two faces of the same coin. In this spirit, the purpose of this paper is to progress towards a global understanding of the problem, and we shall do so by developing a theory of vector-valued nearly additive mappings on semigroups. While a unified theory seems to be out of reach by now, the part of the theory involving quasi-normed groups and maps with values in Banach spaces seems to be ripe with these pages. We hasten to alert the reader that this paper can by no means be considered a survey, although it contains occasional historical comments; two excellent survey papers are [36,52].

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“…where P is a projective resolution of the constant functor O in F(C; O), and where Hom F(C;O) (P, F ) is the cochain complex of O-modules obtained from applying the contravariant functor Hom F(C;O) (−, F ) to the chain complex P. See [6], [7] for more background information on functor cohomology.…”

Section: Typeset By a M S-t E Xmentioning

confidence: 99%

Fusion category algebras

Linckelmann

2004

Journal of Algebra

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This is the unspecified version of the paper.This version of the publication may differ from the final published version. Permanent repository link: Markus LinckelmannAbstract. The fusion system F on a defect group P of a block b of a finite group G over a suitable p-adic ring O does not in general determine the number l(b) of isomorphism classes of simple modules of the block. We show that conjecturally the missing information should be encoded in a single second cohomology class α of the constant functor with value k × on the orbit categoryF c of F-centric subgroups Q of P of b which "glues together" the second cohomology classes α(Q) of AutF (Q)

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A Course in Homological Algebra

Cited by 652 publications

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On universal central extensions of Hom-Lie algebras

On universal central extensions of Hom-Lie algebras

Banach space techniques underpinning a theory for nearly additive mappings

Fusion category algebras

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