Casimir invariants for Hopf algebras

DOI10.1016/0034-4877(92)90007-NzbMath0803.16039OpenAlexW2049012700MaRDI QIDQ2366178

J. R. Links, Mark D. Gould

Publication date: 29 June 1993

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0034-4877(92)90007-n

zbMATH Keywords

inner automorphismsaugmentationbilinear formstrace formsadjoint actionscentral elementsCasimir invariantsquasi-triangular Hopf algebras\(A\)-module homomorphisms\(A\)-modules\(q\)-deformed universal enveloping algebrasfinite- dimensional Ad-invariant submodulesgeneralized Gel'fand invariantsHopf algebra of trace typeinvertible antipode

Mathematics Subject Classification ID

Universal enveloping (super)algebras (17B35) Trace rings and invariant theory (associative rings and algebras) (16R30) Center, normalizer (invariant elements) (associative rings and algebras) (16U70) Smash products of general Hopf actions (16S40)

Related Items (11)

Invariants and matrix elements of the quantum group $U_q[gl(n,\mathbb{C})$ revisited] ⋮ Scalar product for the tensor operators of the quantum algebra Ŭ_q(su₂) by the Wigner–Eckart theorem ⋮ Eigenvalues of Casimir invariants of Uq (gl(m/n)) ⋮ An analogue of Weyl’s law for quantized irreducible generalized flag manifolds ⋮ Quantum double finite group algebras and link polynomials ⋮ Hopf algebra symmetries of an integrable Hamiltonian for anyonic pairing ⋮ Casimir invariants from quasi-Hopf (super)algebras ⋮ Howe duality for the quantum groups Uqu(m,n), Uqu(M) ⋮ The Parthasarathy formula and a spectral triple for the quantum Lagrangian Grassmannian of rank two ⋮ Eigenvalues of Casimir invariants for Uq[osp(m∣n)] ⋮ Hilbert-Schmidt inner product for an adjoint representation of the quantum algebra \(\overset{\smile}{U}_Q(\mathfrak{SU}_2)\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• q-Weyl group and a multiplicative formula for universal R-matrices
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• A \(q\)-analogue of \(U(\mathfrak{gl}(N+1))\), Hecke algebra, and the Yang-Baxter equation
• Finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple Lie algebra
• Casimir invariants and infinitesimal characters for semi-simple Lie algebras
• Identities and characters for finite groups
• Characteristic Identities for Generators of GL(n), O(n) and Sp(n)
• The general U_q(sl(2)) invariant XXZ integrable quantum spin chain

This page was built for publication: Casimir invariants for Hopf algebras