Geodesic
Family algebras
Kirillov, A.1
1 Department of Mathematics, The University of Pennsylvania, Philadelphia, PA 19104
Electronic research announcements of the American Mathematical Society, Tome 06 (2000), pp. 7-20 Cet article a éte moissonné depuis la source American Mathematical Society

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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.
DOI : 10.1090/S1079-6762-00-00075-5

Kirillov, A. 1

1 Department of Mathematics, The University of Pennsylvania, Philadelphia, PA 19104 
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Kirillov, A. Family algebras. Electronic research announcements of the American Mathematical Society, Tome 06 (2000), pp. 7-20. doi: 10.1090/S1079-6762-00-00075-5

[1] Humphreys, James E. Introduction to Lie algebras and representation theory 1972

[2] Kostant, Bertram Lie group representations on polynomial rings Amer. J. Math. 1963 327 404

[3] Vinberg, È. B., Onishchik, A. L. Seminar po gruppam Li i algebraicheskim gruppam 1988 344

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