30 research outputs found
Quantum heaps, cops and heapy categories
A heap is a structure with a ternary operation which is intuitively a group
with forgotten unit element. Quantum heaps are associative algebras with a
ternary cooperation which are to the Hopf algebras what heaps are to groups,
and, in particular, the category of copointed quantum heaps is isomorphic to
the category of Hopf algebras. There is an intermediate structure of a cop in
monoidal category which is in the case of vector spaces to a quantum heap about
what is a coalgebra to a Hopf algebra. The representations of Hopf algebras
make a rigid monoidal category. Similarly the representations of quantum heaps
make a kind of category with ternary products, which we call a heapy category.Comment: 10 pages, an adaptation of an old 2001 preprin
Every quantum minor generates an Ore set
The subset multiplicatively generated by any given set of quantum minors and
the unit element in the quantum matrix bialgebra satisfies the left and right
Ore conditions.Comment: 7 pages; v2: Lemma 1 corrected; part Lemma 1 (iii) adde
Exponential Formulas and Lie Algebra Type Star Products
Given formal differential operators on polynomial algebra in several
variables , we discuss finding expressions determined by the
equation
and their applications. The expressions for are related to the coproducts
for deformed momenta for the noncommutative space-times of Lie algebra type and
also appear in the computations with a class of star products. We find
combinatorial recursions and derive formal differential equations for finding
. We elaborate an example for a Lie algebra , related to a quantum
gravity application from the literature