TWO PERMANENTS IN THE UNIVERSAL ENVELOPING ALGEBRAS OF THE SYMPLECTIC LIE ALGEBRAS

DOI10.1142/S0129167X09005327zbMath1185.17010arXiv0710.0265OpenAlexW2963431734MaRDI QIDQ3636308

Minoru Itoh

Publication date: 30 June 2009

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0710.0265

zbMATH Keywords

symplectic Lie algebraCapelli identitynon-commutative determinantcentral elements, universal enveloping algebras

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Universal enveloping (super)algebras (17B35)

Related Items (4)

Central elements in the universal enveloping algebras for the split realization of the orthogonal Lie algebras ⋮ Casimir elements from the Brauer-Schur-Weyl duality ⋮ Quantisation and nilpotent limits of Mishchenko–Fomenko subalgebras ⋮ Extensions of the Tensor Algebra and Their Applications

Cites Work

• Unnamed Item
• Capelli identities for reductive dual pairs
• Quantum Berezinian and the classical Capelli identity
• 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 \((\text{O}_M,\text{Sp}_N)\)
• Two determinants in the universal enveloping algebras of the orthogonal Lie algebras
• Sklyanin determinant, Laplace operators, and characteristic identities for classical Lie algebras

This page was built for publication: TWO PERMANENTS IN THE UNIVERSAL ENVELOPING ALGEBRAS OF THE SYMPLECTIC LIE ALGEBRAS