Central elements in the universal enveloping algebras for the split realization of the orthogonal Lie algebras
type: Item
instance of: scholarly article
title: Central elements in the universal enveloping algebras for the split realization of the orthogonal Lie algebras
zbMATH Open document ID: 1118.17002
author: Akihito Wachi
published in: Letters in Mathematical Physics
publication date: 2007-05-31T00:00:00Z
review text: The split realization of \(\mathfrak{o}(M)\) is defined as \(\mathfrak{o}(M)=\{X\in\mathrm{Mat}_n(\mathbb{C}):{}^tXM+MX=0\}\), where \(M\) is the symmetric \(n\times n\)-matrix \((\delta_{i,n+1-j})_{1\leq i,j\leq n}\). For the universal enveloping algebra of \(U(\mathfrak{o}(M))\) the author gives explicit formulae for certain central elements. The main ingredients of the formulae are certain column determinants. It is further proved that these central elements form a generating set of the center of \(U(\mathfrak{o}(M))\).
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 17B35
Mathematics Subject Classification ID: 17B10
zbMATH DE Number: 5159803
zbMATH Keywords: orthogonal Lie algebra
zbMATH Keywords: central element
zbMATH Keywords: column determinant
zbMATH Keywords: split realization
MaRDI profile type: Publication
full work available at URL: s11005-006-0082-6
OpenAlex ID: W2049486543
cites work: The Capelli identity, the double commutant theorem, and multiplicity-free actions
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cites work: On central elements in the universal enveloping algebras of the orthogonal Lie algebras
cites work: Q5535148
cites work: Sklyanin determinant, Laplace operators, and characteristic identities for classical Lie algebras
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cites work: Capelli elements in the classical universal enveloping algebras
DOI: 10.1007/S11005-006-0082-6
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description: scientific article; zbMATH DE number 5159803