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PBW deformations of a Fomin–Kirillov Algebra and other examples
(Springer, 2018-09-26)
We begin the study of PBW deformations of graded algebras relevant to the theory of Hopf algebras. One of our examples is the Fomin–Kirillov algebra E3. Another one appeared in a paper of García Iglesias and Vay. As a ...
The cohomology ring of the 12-dimensional Fomin-Kirillov algebra
(Academic Press Inc Elsevier Science, 2016-03)
The 12-dimensional Fomin-Kirillov algebra FK3 is defined as the quadratic algebra with generators a, b and c which satisfy the relations a2=b2=c2=0 and ab+bc+ca=0=ba+cb+ac. By a result of A. Milinski and H.-J. Schneider, ...
On the representation theory of the Drinfeld Double of the Fomin-Kirillov Algebra FK 3
(Springer, 2018-09-13)
Let D be the Drinfeld double of FK3#S3 . We have described the simple D-modules in Pogorelsky and Vay (Adv. Math. 301, 423-457, 2016). In the present work, we describe the indecomposable summands of the tensor products ...
Verma and simple modules for quantum groups at non-abelian groups
(Academic Press Inc Elsevier Science, 2016-10)
The Drinfeld double D of the bosonization of a finite-dimensional Nichols algebra B(V) over a finite non-abelian group G is called a quantum group at a non-abelian group. We introduce Verma modules over such a quantum group ...
Quantum function algebras from finite-dimensional Nichols algebras
(European Mathematical Society, 2020-10)
We describe how to find quantum determinants and antipode formulas from braidedvector spaces using the FRT-construction and finite-dimensional Nichols algebras. It improvesthe construction of quantum function algebras using ...
Finite-dimensional pointed Hopf algebras with alternating groups are trivial
(Springer Heidelberg, 2011-05)
It is shown that Nichols algebras over alternating groups Am (m ≥ 5) are infinite dimensional. This proves that any complex finite dimensional pointed Hopf algebra with group of group-likes isomorphic to Am is isomorphic ...