2 7 N ov 2 00 3 PBW bases for a class of braided Hopf algebras ⋆
نویسنده
چکیده
We prove the existence of a basis of Poincaré-Birkhoff-Witt type for braided Hopf algebras R generated by a braided subspace V ⊂ P (R) if the braiding on V fulfils a triangularity condition. We apply our result to pointed Hopf algebras with abelian coradical and to Nichols algebras of low dimensional simple Uq(sl2)-modules.
منابع مشابه
ar X iv : 1 50 2 . 06 47 2 v 1 [ m at h . R A ] 8 N ov 2 01 4 Gröbner - Shirshov bases and PBW theorems ∗
We review some applications of Gröbner-Shirshov bases, including PBW theorems, linear bases of free universal algebras, normal forms for groups and semigroups, extensions of groups and algebras, embedding of algebras.
متن کاملPbw Deformations of Braided Products Chelsea Walton and Sarah Witherspoon
We present new examples of deformations of smash product algebras that arise from Hopf algebra actions on pairs of module algebras. These examples involve module algebras that are Koszul, in which case a PBW theorem we established previously applies. Our construction generalizes several ‘double’ constructions appearing in the literature, including Weyl algebras and some types of Cherednik algeb...
متن کاملar X iv : m at h / 04 05 17 6 v 3 [ m at h . R T ] 1 7 N ov 2 00 4 QUANTIZED SYMPLECTIC OSCILLATOR ALGEBRAS OF RANK ONE
A quantized symplectic oscillator algebra of rank 1 is a PBW deformation of the smash product of the quantum plane with Uq(sl2). We study its representation theory, and in particular, its category O.
متن کامل2 5 N ov 2 00 8 MODULE CATEGORIES OVER POINTED HOPF ALGEBRAS
We develop some techniques to the study of exact module categories over some families of pointed finite-dimensional Hopf algebras. As an application we classify exact module categories over the tensor category of representations of the small quantum groups uq(sl2).
متن کاملN ov 2 00 3 Symmetric Coalgebras
We construct a structure of a ring with local units on a co-Frobenius coalgebra. We study a special class of co-Frobenius coalgebras whose objects we call symmetric coalgebras. We prove that any semiperfect coalgebra can be embedded in a symmetric coalgebra. A dual version of Brauer's equivalence theorem is presented, allowing a characterization of symmetric coalgebras by comparing certain func...
متن کامل