Frontiers of Mathematics in China >

2011 , Vol. 6 >Issue 4: 789 - 820

DOI: https://doi.org/10.1007/s11464-011-0148-3

RESEARCH ARTICLE

Ideals and simplicity of unitary Lie algebras

  • Yelong ZHENG , 1 ,
  • Zhihua CHANG 2 ,
  • Yun GAO 3
Expand
  • 1. School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China
  • 2. Department of Mathematical and Statistical Science, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada
  • 3. Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3, Canada

Received date: 25 May 2011

Accepted date: 19 Jun 2011

Published date: 01 Aug 2011

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
Fold

Abstract

Double graded ideals and simplicity of elementary unitary Lie algebra eun(R,-,γ) and Steinberg unitary Lie algebra stun(R,-,γ) are characterized, where R is a unital involutory associative algebra over a field F of characteristic zero, n≥5.

Key words： Elementary unitary Lie algebra; Steinberg unitary Lie algebra; graded ideal; graded simplicity; involutory algebra

Cite this article

Yelong ZHENG , Zhihua CHANG , Yun GAO . Ideals and simplicity of unitary Lie algebras[J]. Frontiers of Mathematics in China, 2011 , 6(4) : 789 -820 . DOI: 10.1007/s11464-011-0148-3

References

Publishing order | Descend order by publishing year | Descend order by cited within
1
Allison B N, Faulkner J R. Nonassociative coefficient algebras for Steinberg unitary Lie algebras. J Algebra, 1993, 161: 1-19

DOI

2
Berman S, Gao Y, Krylyuk Y S. Quantum tori and the structure of elliptic quasi-simple Lie algebras. J Functional Analysis, 1996, 135: 339-389

DOI

3
Berman S, Moody R V. Lie algebras graded by finite root systems and the intersection matrix algebras of Slodowy. Invent Math, 1992, 108: 323-347

DOI

4
Faulkner J R. Barbilian planes. Geom Dedicata, 1989, 30: 125-181

DOI

5
Gao Y. Involutive Lie algebras graded by finite root systems and compact forms of IM algebras. Math Z, 1996, 223(4): 651-672

DOI

6
Gao Y. Steiberg unitary Lie algebras and skew-dihedral homology. J Algebra, 1996, 17: 261-304

DOI

7
Helgason S. Differential Geometry, Lie Groups, and Symmetric Spaces. New York: Academic Press, 1978

8
Shang S. Steinberg Lie Algebras and Their Central Extensions. <DissertationTip/>. Hefei: University of Science and Technology of China, 2008

9
Zheng Y. Ideals and Simplicity, Invariant Forms and Derivation Algebra of Unitary Lie Algebras. <DissertationTip/>. Hefei: University of Science and Technology of China, 2009

Options
Outlines

/

〈 〉