New solutions for Yang-Baxter systems.

Nichita, Florin Felix

Displaying similar documents to “New solutions for Yang-Baxter systems.”

A $q$ -analogue of the centralizer construction and skew representations of the quantum affine algebra.

Hopkins, Mark J., Molev, Alexander I. (2006)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Similarity:

$T$ -systems and $Y$ -systems for quantum affinizations of quantum Kac-Moody algebras.

Kuniba, Atsuo, Nakanishi, Tomoki, Suzuki, Junji (2009)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Similarity:

Quantum symmetries in noncommutative C*-systems

Marcin Marciniak (1998)

Banach Center Publications

Similarity:

We introduce the notion of a completely quantum C*-system (A,G,α), i.e. a C*-algebra A with an action α of a compact quantum group G. Spectral properties of completely quantum systems are investigated. In particular, it is shown that G-finite elements form the dense *-subalgebra of A. Furthermore, properties of ergodic systems are studied. We prove that there exists a unique α-invariant state ω on A. Its properties are described by a family of modular operators ${σ_{z}}_{z \in ℂ}$ acting on . It turns...

Left-covariant differential calculi on $S L_{q} (N)$

Konrad Schmüdgen, Axel Schüler (1997)

Banach Center Publications

Similarity:

We study $N^{2} - 1$ dimensional left-covariant differential calculi on the quantum group $S L_{q} (N)$ . In this way we obtain four classes of differential calculi which are algebraically much simpler as the bicovariant calculi. The algebra generated by the left-invariant vector fields has only quadratic-linear relations and posesses a Poincaré-Birkhoff-Witt basis. We use the concept of universal (higher order) differential calculus associated with a given left-covariant first order differential calculus....

Dynamical $ℛ$ matrices of elliptic quantum groups and connection matrices for the $q$ -KZ equations.

Konno, Hitoshi (2006)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Similarity:

$q$ -analog of Gelfand-Graev basis for the noncompact quantum algebra $U_{q} (u (n, 1))$ .

Asherova, Raisa M., Burdík, Čestmír, Havlíček, Miloslav, Smirnov, Yuri F., Tolstoy, Valeriy N. (2010)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Similarity:

Generalized Hurwitz maps of the type S × V → W, anti-involutions, and quantum braided Clifford algebras

Julian Ławrynowicz, Jakub Rembieliński, Francesco Succi (1996)

Banach Center Publications

Similarity:

The notion of a $J^{3}$ -triple is studied in connection with a geometrical approach to the generalized Hurwitz problem for quadratic or bilinear forms. Some properties are obtained, generalizing those derived earlier by the present authors for the Hurwitz maps S × V → V. In particular, the dependence of each scalar product involved on the symmetry or antisymmetry is discussed as well as the configurations depending on various choices of the metric tensors of scalar products of the basis elements....

Differential calculus on 'non-standard' (h-deformed) Minkowski spaces

José de Azcárraga, Francisco Rodenas (1997)

Banach Center Publications

Similarity:

The differential calculus on 'non-standard' h-Minkowski spaces is given. In particular it is shown that, for them, it is possible to introduce coordinates and derivatives which are simultaneously hermitian.

Quantum symmetries for exceptional $S U (4)$ modular invariants associated with conformal embeddings.

Coquereaux, Robert, Schieber, Gil (2009)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Similarity:

Quantum Itô B*-algebras, their classification and decomposition

V. Belavkin (1998)

Banach Center Publications

Similarity:

A simple axiomatic characterization of the general (infinite dimensional, noncommutative) Itô algebra is given and a pseudo-Euclidean fundamental representation for such algebra is described. The notion of Itô B*-algebra, generalizing the C*-algebra, is defined to include the Banach infinite dimensional Itô algebras of quantum Brownian and quantum Lévy motion, and the B*-algebras of vacuum and thermal quantum noise are characterized. It is proved that every Itô algebra is canonically...