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Oleg Ogievetsky

Publications and source records attributed to Oleg Ogievetsky.

24 records · Page 2Linked to original sources
arXiv2005

Orthogonal and Symplectic Quantum Matrix Algebras and Cayley-Hamilton Theorem for them

For families of orthogonal and symplectic types quantum matrix (QM-) algebras, we derive corresponding versions of the Cayley-Hamilton theorem. For a wider family of Birman-Murakami-Wenzl type QM-algebras, we investigate a structure of its characteristic subalgebra (the subalgebra in which the coefficients of characteristic polynomials take values). We define 3 sets of generating elements of the characteristic subalgebra and derive recursive Newton and Wronski relations between them. For the family of the orthogonal type QM-algebras, additional reciprocal relations for the generators of the characteristic subalgebra are obtained.

math.QA↗
arXiv1999

On Inflation Rules for Mosseri-Sadoc Tilings

We give the inflation rules for the decorated Mosseri-Sadoc tiles in the projection class of tilings ${\cal T}^{(MS)}$. Dehn invariants related to the stone inflation of the Mosseri-Sadoc tiles provide eigenvectors of the inflation matrix with eigenvalues equal to $τ= \frac{1+\sqrt{5}}{2}$ and $-τ^{-1}$.

math-ph↗
arXiv1999

On Quasiperiodic Space Tilings, Inflation and Dehn Invariants

We introduce Dehn invariants as a useful tool in the study of the inflation of quasiperiodic space tilings. The tilings by ``golden tetrahedra'' are considered. We discuss how the Dehn invariants can be applied to the study of inflation properties of the six golden tetrahedra. We also use geometry of the faces of the golden tetrahedra to analyze their inflation properties. We give the inflation rules for decorated Mosseri-Sadoc tiles in the projection class of tilings ${\cal T}^{(MS)}$. The Dehn invariants of the Mosseri-Sadoc tiles provide two eigenvectors of the inflation matrix with eigenvalues equal to $τ= \frac{1+\sqrt{5}}{2}$ and $-\frac{1}τ$, and allow to reconstruct the inflation matrix uniquely.

math-ph↗
arXiv1994

Classification of the GL(3) Quantum Matrix Groups

We define quantum matrix groups GL(3) by their coaction on appropriate quantum planes and the requirement that the Poincare series coincides with the classical one. It is shown that this implies the existence of a Yang-Baxter operator. Exploiting stronger equations arising at degree four of the algebra, we classify all quantum matrix groups GL(3). We find 26 classes of solutions, two of which do not admit a normal ordering. The corresponding R-matrices are given.

q-alg↗
arXiv1992

Classical Isomorphisms for Quantum Groups

The expressions for the $\hat{R}$--matrices for the quantum groups SO$_{q^2}$(5) and SO$_q$(6) in terms of the $\hat{R}$--matrices for Sp$_q$(2) and SL$_q$(4) are found, and the local isomorphisms of the corresponding quantum groups are established.

hep-th↗