123 citations · 249 across the 30 of their papers we have counts for
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Chains of twists for symplectic Lie algebras
David Ananikian, Petr Kulish, Vladimir Lyakhovsky
Serious difficulties arise in the construction of chains of twists for symplectic Lie algebras. Applying the canonical chains of extended twists to deform the Hopf algebras U(sp(N)…
Quantum Jordanian twist
Vladimir Lyakhovsky, Alexandr Mirolubov, Mariano del Olmo
The quantum deformation of the Jordanian twist F_qJ for the standard quantum Borel algebra U_q(B) is constructed. It gives the family U_qJ(B) of quantum algebras depending on param…
Full chains of twists for orthogonal algebras
Petr P. Kulish, Vladimir D. Lyakhovsky, Alexander A. Stolin
We show that for some Hopf subalgebras in U_F(so(M)) nontrivially deformed by a twist F it is possible to find the nonlinear primitive copies. This enlarges the possibilities to co…
Jordanian twists on deformed carrier subspaces
Petr P. Kulish, Vladimir D. Lyakhovsky
The nontrivial subspaces with primitive coproducts are found in the deformed universal enveloping algebras. They can form carrier spaces for additional Jordanian twists. The latter…
Twist deformations for Yangians
Vladimir D. Lyakhovsky
It is demonstrated how chains of twists for classical Lie algebras induce the new twist deformations (the deformed Yangians) that quantize the generalized rational solutions of the…
Twist deformations for generalized Heisenberg algebras
Vladimir D. Lyakhovsky
Multidimensional Heisenberg algebras, whose creation and annihilation operators are the N-dimensional vectors, can be injected into simple Lie algebras g. It is demonstrated that t…