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Dominant Dimension and Almost Relatively True Versions of Schur’s Theorem

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Abstract

Perhaps the most fundamental problems of representation theory are to classify and to describe irreducible (=simple) representations and to determine cohomology. It is crucial to develop techniques that allow to transfer information from some (known) cases to other (unknown) cases. A classical result of this kind, due to Schur, recently has been extended widely, and put into a general context. These modern ‘relative’ versions of Schur’s result will be presented. Moreover, the theoretical background behind these results, and the crucial invariant controlling the existence and strength of such equivalences, will be explained, and illustrated by an explicit example. Finally, some open problems will be stated and discussed.

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  1. Mathematisches Institut, Universität zu Köln, Weyertal 86-90, D-50931, Köln, Germany

    Steffen Koenig

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  1. Steffen Koenig
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Correspondence to Steffen Koenig.

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Lecture held in the Seminario Matematico e Fisico on March 30, 2009

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Koenig, S. Dominant Dimension and Almost Relatively True Versions of Schur’s Theorem. Milan J. Math. 78, 457–479 (2010). https://doi.org/10.1007/s00032-010-0130-7

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