Double Bicrossproduct Lie Bialgebras
نویسنده
چکیده
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 appendix, we gave braided diagram calculus for the theory of braided Lie bialgebras. 2000 Mathematics Subject Classification: 18D35, 17B62
منابع مشابه
Double Cross Biproduct and Bicycle Bicrossproduct Lie Bialgebras
We construct double cross biproduct and bicycle bicrossproduct Lie bialgebras from braided Lie bialgebras. The main result generalizes Majid’s matched pair of Lie algebras, Drinfeld’s quantum double, and Masuoka’s cross product Lie bialgebras. 2000 Mathematics Subject Classification: 17B62, 18D35
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 of Complex Type and Associated Poisson Lie Groups
In this work we study a particular class of Lie bialgebras arising from Hermitian structures on Lie algebras such that the metric is ad-invariant. We will refer to them as Lie bialgebras of complex type. These give rise to Poisson Lie groups G whose corresponding duals G∗ are complex Lie groups. We also prove that a Hermitian structure on g with ad-invariant metric induces a structure of the sa...
متن کاملDrinfel’d Doubles and Ehresmann Doubles for Lie Algebroids and Lie Bialgebroids
We show that the Manin triple characterization of Lie bialgebras in terms of the Drinfel’d double may be extended to arbitrary Poisson manifolds and indeed Lie bialgebroids by using double cotangent bundles, rather than the direct sum structures (Courant algebroids) utilized for similar purposes by Liu, Weinstein and Xu. This is achieved in terms of an abstract notion of double Lie algebroid (w...
متن کاملGeneralized Lie Bialgebras and Jacobi Structures on Lie Groups
We study generalized Lie bialgebroids over a single point, that is, generalized Lie bialgebras. Lie bialgebras are examples of generalized Lie bialgebras. Moreover, we prove that the last ones can be considered as the infinitesimal invariants of Lie groups endowed with a certain type of Jacobi structures. We also propose a method to obtain generalized Lie bialgebras. It is a generalization of t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009