1 citations · 1 across the 5 of their papers we have counts for
5 papers
Cocycle Deformations of Algebraic Identities and R-matrices
J. Scott Carter, Alissa Crans, Mohamed Elhamdadi +1
For an arbitrary identity L=R between compositions of maps L and R on tensors of vector spaces V, a general construction of a 2-cocycle condition is given. These 2-cocycles corresp…
Cohomology of Frobenius Algebras and the Yang-Baxter Equation
J. Scott Carter, Alissa S. Crans, Mohamed Elhamdadi +2
A cohomology theory for multiplications and comultiplications of Frobenius algebras is developed in low dimensions in analogy with Hochschild cohomology of bialgebras based on defo…
Musical Actions of Dihedral Groups
Alissa S. Crans, Thomas M. Fiore, Ramon Satyendra
The sequence of pitches which form a musical melody can be transposed or inverted. Since the 1970s, music theorists have modeled musical transposition and inversion in terms of an…
Cohomology of the adjoint of Hopf algebras
J. Scott Carter, Alissa S. Crans, Mohamed Elhamdadi +1
A cohomology theory of the adjoint of Hopf algebras, via deformations, is presented by means of diagrammatic techniques. Explicit calculations are provided in the cases of group al…
Lie 2-Algebras
Alissa S. Crans
We categorify the theory of Lie algebras beginning with a new notion of categorified vector space, or `2-vector space', which we define as an internal category in Vect, the categor…