The graded ring of quantum theta functions for noncommutative torus with real multiplication

Details The graded ring of quantum theta functions for noncommutative torus with real multiplication The graded ring of quantum theta functions for noncommutative torus with real multiplication

2006-01-17

arxiv.org/abs/math/0601405v3

Mathematics

Quantum Algebra

Scientific paper

For quantum torus generated by unitaries $UV = e(\theta)VU$ there exist nontrivial strong Morita autoequivalences in case when $\theta$ is real quadratic irrationality. A.Polishchuk introduced and studied the graded ring of holomorphic sections of powers of the respective bimodule (depending on the choice of a complex structure). We consider a Segre square of this ring whose graded components are spanned by Rieffel scalar products of Polishchuk's holomorphic vectors. These graded components are linear spaces of quantum theta functions in sense of Yu.Manin.

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