q-Deformation of W(2,2) Lie algebra associated with quantum groups

Abstract

An explicit realization of the W(2,2) Lie algebra is presented using the famous bosonic and fermionic oscillators in physics, which is then used to construct the q-deformation of this Lie algebra. Furthermore, the quantum group structures on the q-deformation of this Lie algebra are completely determined.

12 pages

References in corpus (9)

• Deformations of Lie Algebras using $\sigma$-derivations
• Lie bialgebras of generalized Witt type
• Classification of irreducible weight modules over $W$-algebra W(2,2)
• q-Deformed quantum Lie algebras
• Classification of Harish-Chandra modules over the $W$-algebra W(2,2)
• Hamiltonian type Lie bialgebras
• The derivations, central extensions and automorphism group of the Lie algebra $W$
• q-Witt Algebras, q-Virasoro algebra, q-Lie Algebras, q-Holomorph Structure and Representations
• Quantum group structure of the q-deformed $W$ algebra $\WW_q$

Cited by in corpus (2)

• Low dimensional cohomology of Hom-Lie algebras and q-deformed W(2,2) algebra
• Biderivations of Hom-Lie algebras and superalgebras