Invariant Symmetric Bilinear Forms and Derivation Algebras of Unitary Lie Algebras-Reference-Cited by-同舟云学术

Invariant Symmetric Bilinear Forms and Derivation Algebras of Unitary Lie Algebras

Published:2016-06-20 Issue:03 Volume:23 Page:361-384
ISSN:1005-3867
Container-title:Algebra Colloquium
language:en
Short-container-title:Algebra Colloq.

Author:

Zheng Yelong¹,Gao Jiwen²,Chang Zhihua³,Gao Yun⁴

Affiliation:

1. School of Mathematical Sciences and Wu Wen-Tsun Key Laboratory of Mathematics of Chinese Academy of Sciences, University of Science and Technology of China, Hefei 230026, China

2. Department of Basic Courses, Hefei College of Finance and Economics, Hefei 230601, China

3. Department of Mathematical and Statistical Science, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada

4. Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3, Canada

Abstract

Invariant symmetric bilinear forms and derivation algebras of a unitary Lie algebra L over R are characterized: ℬ(L) ≅ (R+/([R,R] ∩ R+))* and Der (L) = Inn (L)+ Der (L)0 = Inn (L)+ SDer (R), which recover what of the special linear Lie algebra and Steinberg Lie algebra over R, where R is a unital involutory associative algebra over a field 𝔽.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1005386716000377

Reference10 articles.

1. Nonassociative Coefficient Algebras for Steinberg Unitary Lie Algebras

2. Quantum Tori and the Structure of Elliptic Quasi-simple Lie Algebras

3. Universal Central Extensions of Twisted and Untwisted Lie Algebras Extended over Commutative Rings

4. Lie algebras graded by finite root systems and the intersection matrix algebras of Slodowy

5. Finite dimensional irreducible representations of elementary unitary Lie algebras over quantum tori

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