منابع مشابه
Strongly Homotopy Lie Bialgebras and Lie Quasi-bialgebras
Structures of Lie algebras, Lie coalgebras, Lie bialgebras and Lie quasibialgebras are presented as solutions of Maurer-Cartan equations on corresponding governing differential graded Lie algebras using the big bracket construction of Kosmann-Schwarzbach. This approach provides a definition of an L∞-(quasi)bialgebra (strongly homotopy Lie (quasi)bialgebra). We recover an L∞-algebra structure as...
متن کاملDouble Bicrossproduct Lie Bialgebras
We construct double biproduct, bicrossproduct, double crossproduct, double bicrossproduct Lie bialgebras from braided Lie bialgebras. The relations between them are found. The main result generalizes Majid’s matched pair of Lie algebras, Drinfeld’s quantum double of Lie bialgebras, and Masuoka’s cross product Lie bialgebras. Some properties of double biproduct Lie bialgebras are given. In the a...
متن کاملBraided Lie Bialgebras
We introduce braided Lie bialgebras as the infinitesimal version of braided groups. They are Lie algebras and Lie coalgebras with the coboundary of the Lie cobracket an infinitesimal braiding. We provide theorems of transmutation, Lie biproduct, bosonisation and double-bosonisation relating braided Lie bialgebras to usual Lie bialgebras. Among the results, the kernel of any split projection of ...
متن کاملLie bialgebras real Cohomology
Let g be a finite dimensional real Lie bialgebra. We introduce an R -valued cohomology of g for which the space of all inequivalent Lie bialgebra central extensions of g by R is isomorphic to that second cohomology group of g . Furthermore, we study the natural projection of this group on the R -valued Lie algebra second cohomology group of g .
متن کاملBiquantization of Lie bialgebras
For any finite-dimensional Lie bialgebra g, we construct a bialgebra Au,v(g) over the ring C[u][[v]], which quantizes simultaneously the universal enveloping bialgebra U(g), the bialgebra dual to U(g), and the symmetric bialgebra S(g). Following [Tur89], we call Au,v(g) a biquantization of S(g). We show that the bialgebra Au,v(g ) quantizing U(g), U(g), and S(g) is essentially dual to the bialg...
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ژورنال
عنوان ژورنال: International Journal of Geometric Methods in Modern Physics
سال: 2017
ISSN: 0219-8878,1793-6977
DOI: 10.1142/s0219887817501420