Decomposition of automorphisms of certain solvable subalgebra of symplectic Lie algebra over commutative rings

Xing Tao Wang; Lei Zhang

doi:10.1155/2012/242736

Decomposition of automorphisms of certain solvable subalgebra of symplectic Lie algebra over commutative rings

Xing Tao Wang^*
, Lei Zhang

^*Corresponding author for this work

Faculty of Computing

Harbin Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

Let C _l+1(R) be the 2(l + 1) × 2(l + 1) matrix symplectic Lie algebra over a commutative ring R with 2 invertible. Then t _l+1 ^(C)(R) = {m̄ ₁ m̄ ₂ 0 -m̄ ₁ ^T | m̄ ₁ is an l + 1 upper triangular matrix, m̄ ₂ ^T = m̄ ₂, over R} is the solvable subalgebra of C _l+1(R). In this paper, we give an explicit description of the automorphism group of t _l+1 ^(C)(R).

Original language	English
Article number	242736
Journal	International Journal of Mathematics and Mathematical Sciences
Volume	2012
DOIs	https://doi.org/10.1155/2012/242736
State	Published - 2012

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title = "Decomposition of automorphisms of certain solvable subalgebra of symplectic Lie algebra over commutative rings",

abstract = "Let C l+1(R) be the 2(l + 1) × 2(l + 1) matrix symplectic Lie algebra over a commutative ring R with 2 invertible. Then t l+1 (C)(R) = \{{\=m} 1 {\=m} 2 0 -{\=m} 1 T | {\=m} 1 is an l + 1 upper triangular matrix, {\=m} 2 T = {\=m} 2, over R\} is the solvable subalgebra of C l+1(R). In this paper, we give an explicit description of the automorphism group of t l+1 (C)(R).",

author = "Wang, \{Xing Tao\} and Lei Zhang",

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AU - Zhang, Lei

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N2 - Let C l+1(R) be the 2(l + 1) × 2(l + 1) matrix symplectic Lie algebra over a commutative ring R with 2 invertible. Then t l+1 (C)(R) = {m̄ 1 m̄ 2 0 -m̄ 1 T | m̄ 1 is an l + 1 upper triangular matrix, m̄ 2 T = m̄ 2, over R} is the solvable subalgebra of C l+1(R). In this paper, we give an explicit description of the automorphism group of t l+1 (C)(R).

AB - Let C l+1(R) be the 2(l + 1) × 2(l + 1) matrix symplectic Lie algebra over a commutative ring R with 2 invertible. Then t l+1 (C)(R) = {m̄ 1 m̄ 2 0 -m̄ 1 T | m̄ 1 is an l + 1 upper triangular matrix, m̄ 2 T = m̄ 2, over R} is the solvable subalgebra of C l+1(R). In this paper, we give an explicit description of the automorphism group of t l+1 (C)(R).

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DO - 10.1155/2012/242736

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JO - International Journal of Mathematics and Mathematical Sciences

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ER -

Decomposition of automorphisms of certain solvable subalgebra of symplectic Lie algebra over commutative rings

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