Seminar on low-dimensional mathematics
November 24, 2006

Emil Akhmedov, ITEP
Exponentiation of cubical matrices

We define exponent of cubic massives of numbers.
The role of unity matrix in this case is played
by cubic matrix whose elements are structure constants
of associative semi-simple algebra. Hence,
the coefficients of the Teylor expansion of this new
"surface" exponent in powers of the cubic massive are related to the
two dimensional simplicial topological invariants.
Accordingly all the possible exponents are classified
by two dimensional topologies. We discuss the application
of this "surface" exponent to the alternative definition of
lattice integrable models and to the construction
of the solutions of the Yang-Baxter equation. 

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