5 papers
Multilinear quantum Lie operations
V. K. Kharchenko
It is shown that the dimension of the multilinear quantum Lie operations space is either equal to zero or included between and The lower bound is achieved if the…
An Algebra of Skew Primitive Elements
V. K. Kharchenko
We study the various term operations on the set of skew primitive elements of Hopf algebras, generated by skew primitive semi-invariants of an Abelian group of grouplike elements.…
A quantum analog of the Poincare-Birkhoff-Witt theorem
Vladislav Kharchenko
We reduce the basis construction problem for Hopf algebras generated by skew-primitive semi-invariants to a study of special elements, called ``super-letters,'' which are defined b…
A combinatorial approach to quantification of Lie algebras
V. K. Kharchenko
We propose a notion of a quantum universal enveloping algebra for an arbitrary Lie algebra defined by generators and relations which is based on the quantum Lie operation concept.…
Actions of GL_q(2,C) on C(1,3) and its four dimensional representations
V. K. Kharchenko, Jaime Keller, S. Rodriguez-Romo
A complete classification is given of all inner actions on the Clifford algebra C(1,3) defined by representations of the quantum group GL_q(2,C), q^m\neq 1, which are not reduced t…