Simple and semisimple Lie algebras

and codimension growth

Authors:
Antonio Giambruno, Amitai Regev and Michail V. Zaicev

Journal:
Trans. Amer. Math. Soc. **352** (2000), 1935-1946

MSC (2000):
Primary 17B01, 17B20, 16R10; Secondary 20C30, 17C05

DOI:
https://doi.org/10.1090/S0002-9947-99-02419-8

Published electronically:
December 14, 1999

MathSciNet review:
1637070

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We study the exponential growth of the codimensions of a finite dimensional Lie algebra over a field of characteristic zero. In the case when is semisimple we show that exists and, when is algebraically closed, is equal to the dimension of the largest simple summand of . As a result we characterize central-simplicity: is central simple if and only if .

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Additional Information

**Antonio Giambruno**

Affiliation:
Department of Mathematics, University of Palermo, Via Archirafi 34, 90123 Palermo, Italy

Email:
a.giambruno@unipa.it

**Amitai Regev**

Affiliation:
Department of Theoretical Mathematics, The Weizmann Institute of Science, Rehovot 76100, Israel and The Pennsylvania State University, University Park, Pennsylvania 16802

Email:
regev@wisdom.weizmann.ac.il, regev@math.psu.edu

**Michail V. Zaicev**

Affiliation:
Department of Mechanics and Mathematics, Moscow State University, Moscow 119899, Russia

Email:
zaicev@nw.math.msu.su

DOI:
https://doi.org/10.1090/S0002-9947-99-02419-8

Keywords:
Lie algebras,
polynomial identities,
codimensions

Received by editor(s):
November 27, 1997

Published electronically:
December 14, 1999

Additional Notes:
The first author was partially supported by MURST and CNR of Italy

The second author was partially supported by NSF Grant No. DMS-94-01197

The third author was partially supported by RFFI grants 96-01-00146 and 96-15-96050

Article copyright:
© Copyright 2000
American Mathematical Society