Ideals and simplicity of unitary Lie algebras

Abstract

Double graded ideals and simplicity of elementary unitary Lie algebra \mathfrak{e}{\mathfrak{u}}_n(R{,}^{-},\mathrm{\gamma }) and Steinberg unitary Lie algebra \mathfrak{s}\mathfrak{t}{\mathfrak{u}}_n(R{,}^{-},\mathrm{\gamma }) are characterized, where R is a unital involutory associative algebra over a field \mathfrak{F} of characteristic zero, n≥5.

Keywords

Elementary unitary Lie algebra / Steinberg unitary Lie algebra / graded ideal / graded simplicity / involutory algebra

References

[1] Allison B N, Faulkner J R. Nonassociative coefficient algebras for Steinberg unitary Lie algebras. J Algebra, 1993, 161: 1-19

[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

[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

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

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

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

[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

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