Two determinants in the universal enveloping algebras of the orthogonal Lie algebras

DOI10.1016/j.jalgebra.2006.11.033zbMath1155.17003OpenAlexW2090327437WikidataQ115351491 ScholiaQ115351491MaRDI QIDQ2382995

Minoru Itoh

Publication date: 5 October 2007

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2006.11.033

zbMATH Keywords

Capelli identitycentral elements of universal enveloping algebrasOrthogonal Lie algebras

Mathematics Subject Classification ID

Universal enveloping (super)algebras (17B35)

Related Items (4)

Casimir elements from the Brauer-Schur-Weyl duality ⋮ TWO PERMANENTS IN THE UNIVERSAL ENVELOPING ALGEBRAS OF THE SYMPLECTIC LIE ALGEBRAS ⋮ Quantisation and nilpotent limits of Mishchenko–Fomenko subalgebras ⋮ Extensions of the Tensor Algebra and Their Applications

Cites Work

• The Capelli identity, the double commutant theorem, and multiplicity-free actions
• Central elements in the universal enveloping algebras for the split realization of the orthogonal Lie algebras
• Capelli identities for classical Lie algebras
• Capelli identities for the dual pair \((\text{O}_M,\text{Sp}_N)\)
• Erratum to "Remarks on Classical Invariant Theory"
• Yangians and classical Lie algebras
• Sklyanin determinant, Laplace operators, and characteristic identities for classical Lie algebras
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