Higher-dimensional algebra is the study of generalizations of algebraic concepts obtained through a process called ‘categorification’. My research in higher-dimensional algebra develops and...
Cohomology of Frobenius Algebras and the Yang-Baxter Equation (2008)
Carter, J. Scott, Crans, Alissa S., Elhamdadi, Mohamed, Karadayi, Enver, Saito, Masahico
A cohomology theory for multiplications and comultiplications of Frobenius algebras is developed in low dimensions in analogy with Hochschild cohomology of bialgebras based on deformation theory....
Musical Actions of Dihedral Groups (2007)
Crans, Alissa S., Fiore, Thomas M., Satyendra, Ramon
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 action of the...
Cohomology of the adjoint of Hopf algebras (2007)
Carter, J. Scott, Crans, Alissa S., Elhamdadi, Mohamed, Saito, Masahico
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 algebras, function...
Exotic Statistics for Strings in 4d BF Theory (2006)
Baez, John C., Wise, Derek K., Crans, Alissa S.
After a review of exotic statistics for point particles in 3d BF theory, and especially 3d quantum gravity, we show that string-like defects in 4d BF theory obey exotic statistics governed by the...
From Loop Groups to 2-Groups (2005)
Baez, John C., Crans, Alissa S., Stevenson, Danny, Schreiber, Urs
We describe an interesting relation between Lie 2-algebras, the Kac-Moody central extensions of loop groups, and the group String(n). A Lie 2-algebra is a categorified version of a Lie algebra where...
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 category of vector spaces....
Higher-dimensional algebra VI: Lie 2-algebras, The-ory and Applications of Categories 12 (2004)
The theory of Lie algebras can be categorified starting from a new notion of ‘2-vector space’, which we define as an internal category in Vect. There is a 2-category 2Vect having these 2-vector...
Higher-Dimensional Algebra VI: Lie 2-Algebras (2003)
Baez, John C., Crans, Alissa S.
The theory of Lie algebras can be categorified starting from a new notion of "2-vector space", which we define as an internal category in Vect. There is a 2-category 2Vect having these 2-vector...