Tetrahedron equation and cyclic quantum dilogarithm identities
@article{Bytsko2013TetrahedronEA, title={Tetrahedron equation and cyclic quantum dilogarithm identities}, author={Andrei Bytsko and A. Yu. Volkov}, journal={arXiv: Quantum Algebra}, year={2013} }
We establish a hierarchy of quantum dilogarithm identities associated to a sequence of triangular shaped quivers. The tetrahedron equation plays a key role in our construction.
7 Citations
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References
SHOWING 1-10 OF 16 REFERENCES
Classical and Quantum Dilogarithm Identities
- Mathematics
- 2011
Using the quantum cluster algebra formalism of Fock and Goncharov, we present several forms of quantum dilogarithm identities associated with periodicities in quantum cluster algebras, namely, the…
Quantum Dilogarithm
- Physics
- 1993
A quantum generalization of Rogers’ five term, or “pentagon” dilogarithm identity is suggested. It is shown that the classical limit gives usual Rogers’ identity. The case where the quantum identity…
FROM THE TETRAHEDRON EQUATION TO UNIVERSAL R-MATRICES
- Mathematics
- 1998
Modified universal R-matrices, associated with the central ex- tension (through the Drinfeld's double construction) of the quantum groups Uq(slN), are realized through an infinite dimensional…
On cluster theory and quantum dilogarithm identities
- Mathematics
- 2011
These are expanded notes from three survey lectures given at the 14th International Conference on Representations of Algebras (ICRA XIV) held in Tokyo in August 2010. We first study identities…
The quantum dilogarithm and representations of quantum cluster varieties
- Mathematics
- 2009
We construct, using the quantum dilogarithm, a series of *-representations of quantized cluster varieties. This includes a construction of infinite dimensional unitary projective representations of…
Simplex equations and their solutions
- Physics, Mathematics
- 1991
We investigate ann-simplex generalization of the classical and quantum Yang-Baxter equation. For the case ofsl(2) we find the most general solution of the classicaln-simplex equation for alln. These…
Periodicities in cluster algebras and dilogarithm identities
- Mathematics
- 2011
We consider two kinds of periodicities of mutations in cluster algebras. For any sequence of mutations under which exchange matrices are periodic, we define the associated T- and Y-systems. When the…
KP Solitons, Higher Bruhat and Tamari Orders
- Mathematics
- 2012
In a tropical approximation, any tree-shaped line soliton solution, a member of the simplest class of soliton solutions of the Kadomtsev-Petviashvili (KP-II) equation, determines a chain of planar…