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## Reflection equation algebra in braided geometry

Journal of Generalized Lie Theory and Applications. 2008. Vol. 2. No. 3. P. 162-174.

Braided geometry is a sort of the noncommutative geometry related to a braiding. The
central role in this geometry is played by the reflection equation algebra associated with a braiding of the Hecke type. Using this algebra, we introduce braided versions of the Lie algebras gl(n) and sl(n). We further define braided analogs of the coadjoint orbits and the vector fields on a q-hyperboloid which is the simplest example of a ”braided orbit”. Besides, we present a braided version of the Cayley-Hamilton identity generalizing the result of Kantor and Trishin on the super-matrix characteristic identities.

Research target:
Philosophy, Ethics, and Religious Studies

Language:
English

Gurevich D., Pyatov P. N., Saponov P. A., St Petersburg Mathematical Journal 2009 Vol. 20 P. 213-253

Let R : V 2 → V 2 be a Hecke type solution of the quantum Yang-Baxter equation (a
Hecke symmetry). Then, the Hilbert-Poincr´e series of the associated R-exterior algebra of the space V is a ratio of two polynomials of degree m (numerator) and n (denominator).
Assuming R to be skew-invertible, we define a rigid quasitensor ...

Added: October 16, 2012

Pyatov P. N., Isaev A. P., Ogievetsky O., Journal of Physics A: Mathematical and Theoretical 1999 Vol. 32 P. 115-121

The Cayley-Hamilton-Newton identities which generalize both the characteristic identity and the Newton relations have been recently obtained for the algebras of the RTT-type. We extend this result to a wider class of algebras M(ˆR, ˆ F) defined by a pair of compatible
solutions of the Yang-Baxter equation. This class includes the RTT-algebras as well as the ...

Added: October 16, 2012

Rudakov A. N., Journal of Algebraic Geometry 1997 Vol. 197 No. 1 P. 231-245

The main goal of the article is to give the definition of algebraic stability that
would permit us to consider stability, not only for algebraic vector bundles or
torsion-free coherent sheaves, but for the abelian category of coherent sheaves or
for whatever abelian category. We present an axiomatic description of the algebraic
stability on an abelian category and prove ...

Added: October 16, 2012

Feigin B. L., Rybnikov L. G., Frenkel E., Duke Mathematical Journal 2010 Vol. 155 No. 2 P. 337-363

"The universal enveloping algebra of any simple Lie algebra g contains a
family of commutative subalgebras, called the quantum shift of argument
subalgebras math.RT/0606380 , math.QA/0612798 . We prove that generically their
action on finite-dimensional modules is diagonalizable and their joint spectra
are in bijection with the set of monodromy-free opers for the Langlands dual ...

Added: October 12, 2012

Moraru R., Verbitsky M., Central European Journal of Mathematics 2010 Vol. 8 No. 2 P. 327-337

Added: October 12, 2012

Tyurin N. A., Theoretical and Mathematical Physics 2011 Vol. 167 No. 2 P. 567-576

Added: October 18, 2012

Nekrasov N., Marshakov A., Journal of High Energy Physics 2007 No. 0701 P. 104

Added: October 18, 2012

Braverman A., Finkelberg M. V., Duke Mathematical Journal 2010 Vol. 152 No. 1 P. 175-206

This paper is the first in a series that describe a conjectural analog of the geometric Satake isomorphism for an affine Kac-Moody group (in this paper for simplicity we consider only untwisted and simply connected case). The usual geometric Satake isomorphism for a reductive group G identifies the tensor category Rep(G_) of finitedimensional representations of ...

Added: October 12, 2012

Zabrodin A., Physica D: Nonlinear Phenomena 2007 No. 235 P. 101-108

Added: October 18, 2012

Mineev-Weinstein M., Abanov A., Zabrodin A., Physica D: Nonlinear Phenomena 2007 No. 235 P. 62-71

Added: October 18, 2012

Zotov A., Levin A., Olshanetsky M., Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 2009 Vol. 5 No. 065 P. 1-22

Modifications of bundles over complex curves is an operation that allows one to
construct a new bundle from a given one. Modifications can change a topological type of
bundle. We describe the topological type in terms of the characteristic classes of the bundle.Being applied to the Higgs bundles modifications establish an equivalence between different classical integrable systems. ...

Added: October 15, 2012

Feigin E., Fourier G., Littelmann P., International Mathematics Research Notices 2011 Vol. 2011 No. 24 P. 5760-5784

We study the PBW filtration on the highest weight representations V(λ) of sp2n. This
filtration is induced by the standard degree filtration on U(n−). We give a description
of the associated graded S(n−)-module gr V(λ) in terms of generators and relations. We
also construct a basis of gr V(λ). As an application we derive a graded combinatorial
formula for ...

Added: October 12, 2012

Goldengorin B. I., European Journal of Operational Research 2009 Vol. 198 No. 1 P. 102-112

Added: July 31, 2012

Goldengorin B. I., Ghosh D., Journal of Global Optimization 2005 Vol. 32 No. 1 P. 65-82

Added: July 31, 2012

Finkelberg M. V., Gaitsgory D., Kuznetsov A., Publications of the Research Institute for Mathematical Sciences 2003 Vol. 39 No. 4 P. 721-766

Added: October 12, 2012

Kolesnikov A., Banakh T., Bogachev V., Functional Analysis and Its Applications 2004 P. 23-47

Added: October 12, 2012

Rudakov A. N., Шафаревич И., Успехи математических наук 1978 Т. 33 № 1(199) С. 227-228

Added: October 16, 2012

Rudakov A. N., Шафаревич И., Успехи математических наук 1978 Т. 33 № 6(204) С. 231-232

Added: October 16, 2012

Marshakov A., Theoretical and Mathematical Physics 2011 Vol. 169 No. 3 P. 1704-1723

Added: October 18, 2012

Liviu O., Verbitsky M., International Mathematics Research Notices 2012 No. 4 P. 894-903

A manifold M is locally conformally Kähler (LCK), if it admits a Kähler covering with monodromy acting by holomorphic homotheties. For a compact connected group G acting on an LCK manifold by holomorphic automorphisms, an averaging procedure gives a G-invariant LCK metric. Suppose that S1 acts on an LCK manifold M by holomorphic isometries, and ...

Added: October 24, 2012

Amerik E., Proceedings of the Edinburgh Mathematical Society 2011 Vol. 51 No. 1 P. 1-7

Added: October 15, 2012

Series C., Bufetov A. I., Mathematical Proceedings of the Cambridge Philosophical Society 2011 Vol. 151 No. 1 P. 145-159

We use Series' Markovian coding for words in Fuchsian groups and the
Bowen-Series coding of limit sets to prove an ergodic theorem for Cesaro averages of
spherical averages in a Fuchsian group. ...

Added: October 18, 2012

Alcaraz F. C., Pyatov P. N., Rittenberg V., Journal of Statistical Mechanics: Theory and Experiment 2008 Vol. P01006 P. 1-38

We consider the raise and peel model of a one-dimensional fluctuating interface in
the presence of an attractive wall. The model can also describe a pair annihilation
process in a disordered unquenched media with a source at one end of the system. For
the stationary states, several density profiles are studied usingMonte Carlo simulations. We point out a ...

Added: October 16, 2012

Turkensteen M., Ghosh D., Goldengorin B. I. et al., European Journal of Operational Research 2008 Vol. 189 No. 3 P. 775-788

Added: July 31, 2012