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Electronic Research Announcements
ISSN 1079-6762

 

Family algebras


Author: A. A. Kirillov
Journal: Electron. Res. Announc. Amer. Math. Soc. 6 (2000), 7-20
MSC (2000): Primary 15A30, 22E60
Published electronically: March 1, 2000
MathSciNet review: 1745518
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Abstract: A new class of associative algebras is introduced and studied. These algebras are related to simple complex Lie algebras (or root systems). Roughly speaking, they are finite dimensional approximations to the enveloping algebra $U(\mathfrak{g})$ viewed as a module over its center.

It seems that several important questions on semisimple algebras and their representations can be formulated, studied and sometimes solved in terms of our algebras.

Here we only start this program and hope that it will be continued and developed.


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Additional Information

A. A. Kirillov
Affiliation: Department of Mathematics, The University of Pennsylvania, Philadelphia, PA 19104
Email: kirillov@math.upenn.edu

DOI: http://dx.doi.org/10.1090/S1079-6762-00-00075-5
PII: S 1079-6762(00)00075-5
Keywords: Enveloping algebras, invariants, representations of semisimple Lie algebras
Received by editor(s): December 31, 1999
Published electronically: March 1, 2000
Communicated by: Svetlana Katok
Article copyright: © Copyright 2000 American Mathematical Society