Lie bialgebra contractions and quantum deformations of quasi‐orthogonal algebras
نویسندگان
چکیده
منابع مشابه
Lie bialgebra contractions and quantum deformations of quasi-orthogonal algebras
Lie bialgebra contractions are introduced and classified. A non-degenerate coboundary bialgebra structure is implemented into all pseudo-orthogonal algebras so(p, q) starting from the one corresponding to so(N +1). It allows to introduce a set of Lie bialgebra contractions which leads to Lie bialgebras of quasi-orthogonal algebras. This construction is explicitly given for the cases N = 2, 3, 4...
متن کاملDeformations and contractions of Lie algebras
We discuss the mutually opposite procedures of deformations and contractions of Lie algebras. Our main purpose is to illustrate the fact that, with appropriate combinations of both procedures, we obtain new Lie algebras. Firstly, we discuss low-dimensional Lie algebras, and these simple examples illustrate that, whereas for every contraction there exists a reverse deformation, the converse is n...
متن کاملOn Deformations and Contractions of Lie Algebras
In this contributed presentation, we discuss and compare the mutually opposite procedures of deformations and contractions of Lie algebras. We suggest that with appropriate combinations of both procedures one may construct new Lie algebras. We first discuss low-dimensional Lie algebras and illustrate thereby that whereas for every contraction there exists a reverse deformation, the converse is ...
متن کاملBialgebra deformations of certain universal enveloping algebras
Let A denote a bialgebra over a field k and let At = A[[t]] denote the ring of formal power series with coefficients in A. Assume that A is a free algebra over k with a basis of primitives. We give a simple construction which makes At a bialgebra deformation of A. Usually At is neither commutative nor cocommutative. This construction yields deformations of bialgebras associated with families of...
متن کاملBialgebra Cohomology, Pointed Hopf Algebras, and Deformations
We give explicit formulas for maps in a long exact sequence connecting bialgebra cohomology to Hochschild cohomology. We give a sufficient condition for the connecting homomorphism to be surjective. We apply these results to compute all bialgebra two-cocycles of certain Radford biproducts (bosonizations). These two-cocycles are precisely those associated to the finite dimensional pointed Hopf a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 1995
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.531368