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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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$\mathfrak {F}$-categories and $\mathfrak {F}$-functors in the representation theory of Lie algebras
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by Ben Cox PDF
Trans. Amer. Math. Soc. 343 (1994), 433-453 Request permission

Abstract:

The fields of algebra and representation theory contain abundant examples of functors on categories of modules over a ring. These include of course Horn, Ext, and Tor as well as the more specialized examples of completion and localization used in the setting of representation theory of a semisimple Lie algebra. In this article we let $\mathfrak {a}$ be a Lie subalgebra of a Lie algebra $\mathfrak {g}$ and $\Gamma$ be a functor on some category of $\mathfrak {a}$-modules. We then consider the following general question: For a $\mathfrak {g}$-module E what hypotheses on $\Gamma$ and E are sufficient to insure that $\Gamma (E)$ admits a canonical structure as a $\mathfrak {g}$-module? The article offers an answer through the introduction of the notion of $\mathfrak {F}$-categories and $\mathfrak {F}$-functors. The last section of the article treats various examples of this theory.
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 343 (1994), 433-453
  • MSC: Primary 17B67; Secondary 17B55
  • DOI: https://doi.org/10.1090/S0002-9947-1994-1191610-7
  • MathSciNet review: 1191610