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Representations of the Kauffman skein algebra II: punctured surfaces
Representations of the Kauffman skein algebra II punctured surfaces Geometric Topology
2012/6/29
In earlier work, we constructed invariants of irreducible representations of the Kauffman skein algebra of a surface. We introduce here an inverse construction, which to a set of possible invariants a...
Representations of the Kauffman skein algebra I: invariants and miraculous cancellations
Representations of the Kauffman skein algebra I invariants miraculous cancellations Geometric Topology
2012/6/29
We study finite-dimensional representations of the Kauffman skein algebra of a surface S. In particular, we construct invariants of such irreducible representations when the underlying parameter q is ...
Funar algebra $K_\infty=K_\infty(\alpha,\beta;k)$ is the quotient of the group algebra over a ring $k$ of the braid group $B_\infty$ by two cubic relations: $\sigma_1^3-\alpha\sigma_1^2+\beta\sigma_1-...
A survey of quantum Teichmüller space and Kashaev algebra
shear coordinate quantum Teichmuller space Kashaev coordinates generalized Kashaev algebra
2011/9/20
Abstract: In this chapter, we survey the algebraic aspects of quantum Teichm\"uller space, generalized Kashaev algebra and a natural relationship between the two algebras.
Abelianizations of derivation Lie algebras of free associative algebra and free Lie algebra
moduli space of curves Lie algebra homology graph homology derivation
2011/9/14
Abstract: We determine the abelianizations of the following three kinds of graded Lie algebras in a certain stable range: derivations of the free associative algebra, derivations of the free Lie algeb...
Homological algebra modulo exact zero-divisors
Exact zero divisors (co)homology complexity
2011/1/21
We study the homological behavior of modules over local rings modulo exact zero-divisors. We obtain new results which are in some sense “opposite” to those known for modules over local rings modulo re...
Finite-dimensional vertex algebra modules over fixed point commutative subalgebras
vertex algebra Galois extension commutative algebra
2011/1/18
Let A be a connected commutative C-algebra with derivation D,G a finite linear automorphism group of A which preserves D, and R = AG the fixed point subalgebra of A under the action of G. We show that...
On solvability of the automorphism group of a finite-dimensional algebra
solvability of the automorphism group finite-dimensional algebra
2011/1/17
Consider an automorphism group of a finite-dimensional algebra. S. Halperin conjectured that the unity component of this group is solvable if the algebra is a complete intersection.
We introduce a new model for the secondary Steenrod algebra at the prime 2 which is both smaller and more accessible than the original construction of H.-J. Baues.
Relative homological algebra in categories of representations of infinite quivers
cover envelope torsion free flat representations of a quiver
2010/11/26
In the first part of this paper, we prove the existence of torsion
free covers in the category of representations of quivers, (Q,R-Mod),for a wide class of quivers included in the class of the so-cal...