By Abdenacer Makhlouf, Eugen Paal, Sergei D. Silvestrov, Alexander Stolin
This booklet collects the complaints of the Algebra, Geometry and Mathematical Physics convention, held on the college of Haute Alsace, France, October 2011. prepared within the 4 components of algebra, geometry, dynamical symmetries and conservation legislation and mathematical physics and functions, the publication covers deformation concept and quantization; Hom-algebras and n-ary algebraic buildings; Hopf algebra, integrable platforms and comparable math constructions; jet conception and Weil bundles; Lie thought and functions; non-commutative and Lie algebra and more.
The papers discover the interaction among examine in modern arithmetic and physics occupied with generalizations of the most constructions of Lie conception aimed toward quantization and discrete and non-commutative extensions of differential calculus and geometry, non-associative buildings, activities of teams and semi-groups, non-commutative dynamics, non-commutative geometry and purposes in physics and beyond.
The publication advantages a extensive viewers of researchers and complex students.
Read Online or Download Algebra, Geometry and Mathematical Physics: AGMP, Mulhouse, France, October 2011 PDF
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Extra resources for Algebra, Geometry and Mathematical Physics: AGMP, Mulhouse, France, October 2011
6). Clearly, F1 is the algebra of regular functions on the connected simply connected group G, whose Lie algebra is g. Let k be a reductive subalgebra of g which contains h and is defined by Γ , K the corresponding subgroup of G, and F(G/K ) the algebra of regular functions on the homogeneous space G/K . According to [11, Theorem 33], we have F(G/K ) = F1  K 1,α . 1 limq⊕1 Fq  K q,α = F(G/K ). Furthermore, since Fq  K q,α is a Hopf module algebra over U , G/K is a Poisson homogeneous space over G equipped with the Poisson-Lie structure defined by the Drinfeld-Jimbo classical r -matrix r0 = ν⊗R+ eν ∀ e−ν .
It often requires insights both in the algebraic structure of the commutation relations and in the properties of the involved classes of operators. In algebraic contexts it often leads to interesting combinatorial identities and problems, while in the context of ⊕-representations (involutive representations) and operator algebras it involves also spectral theory of possibly unbounded operators in the finite-dimensional or infinite-dimensional spaces. The relations (1) provide an interesting example in this respect.
Math. Phys. 272, 635–660 (2007) Commutants and Centers in a 6-Parameter Family of Quadratically Linked Quantum Plane Algebras Fredrik Ekström and Sergei D. Silvestrov Abstract We consider a family of associative algebras, defined as the quotient of a free algebra with the ideal generated by a set of multi-parameter deformed commutation relations between four generators consisting of five quantum plane relations between pairs of generators and one sub-quadratic relation inter-linking all four generators.
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