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4 papers
On contractions of quantum orthogonal groups
N. A. Gromov, I. V. Kostyakov, V. V. Kuratov
The standard Faddeev quantization of the simple groups is modified in such a way that the quantum analogs of the nonsemisimple groups are obtained by contractions. The contracted q…
On root systems in spaces with degenerate metric
I. V. Kostyakov, N. A. Gromov, V. V. Kuratov
A root systems in Carroll spaces with degenerate metric are defined. It is shown that their Cartan matrices and reflection groups are affine. With the help of the geometric conside…
Graded contractions of Virasoro algebras
I. V. Kostyakov, N. A. Gromov, V. V. Kuratov
We describe graded contractions of Virasoro algebra. The highest weight representations of Virasoro algebra are constructed. The reducibility of representations is analysed. In con…
Quantum Orthogonal Cayley-Klein Groups and Algebras
N. A. Gromov, I. V. Kostyakov, V. V. Kuratov
The extension of FRT quantization theory for the nonsemisimple CK groups is suggested. The quantum orthogonal CK groups are realized as the Hopf algebras of the noncommutative func…