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Classifications of star products and deformations of Poisson brackets

Philippe Bonneau (2000)

Banach Center Publications

On the algebra of functions on a symplectic manifold we consider the pointwise product and the Poisson bracket; after a brief review of the classifications of the deformations of these structures, we give explicit formulas relating a star product to its classifying formal Poisson bivector.

Classifying Spaces for Kähler Metrics.

A. ADLER (1963)

Mathematische Annalen

Clifford algebra with Reduce

Brackx, Freddy, Constales, Denis, Delanghe, Richard, Serras, Herman (1987)

Proceedings of the Winter School "Geometry and Physics"

Clifford algebras and possible kinematics.

McRae, Alan S. (2007)

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

Clifford algebras, Möbius transformations, Vahlen matrices, and $B$ -loops

Jimmie Lawson (2010)

Commentationes Mathematicae Universitatis Carolinae

In this paper we show that well-known relationships connecting the Clifford algebra on negative euclidean space, Vahlen matrices, and Möbius transformations extend to connections with the Möbius loop or gyrogroup on the open unit ball $B$ in $n$ -dimensional euclidean space $ℝ^{n}$ . One notable achievement is a compact, convenient formula for the Möbius loop operation $a * b = (a + b) {(1 - a b)}^{- 1}$ , where the operations on the right are those arising from the Clifford algebra (a formula comparable to $(w + z) {(1 + \bar{w} z)}^{- 1}$ for the Möbius loop multiplication...

Clifford and harmonic analysis on cylinders and torii.

Rolf Sören Krausshar, John Ryan (2005)

Revista Matemática Iberoamericana

Cotangent type functions in Rn are used to construct Cauchy kernels and Green kernels on the conformally flat manifolds Rn/Zk where 1 < = k ≤ M. Basic properties of these kernels are discussed including introducing a Cauchy formula, Green's formula, Cauchy transform, Poisson kernel, Szegö kernel and Bergman kernel for certain types of domains. Singular Cauchy integrals are also introduced as are associated Plemelj projection operators. These in turn are used to study Hardy spaces in this...

Clifford approach to metric manifolds

Chisholm, J. S. R., Farwell, R. S. (1991)

Proceedings of the Winter School "Geometry and Physics"

[For the entire collection see Zbl 0742.00067.]For the purpose of providing a comprehensive model for the physical world, the authors set up the notion of a Clifford manifold which, as mentioned below, admits the usual tensor structure and at the same time a spin structure. One considers the spin space generated by a Clifford algebra, namely, the vector space spanned by an orthonormal basis ${e_{j} : j = 1, \dots, n}$ satisfying the condition ${e_{i}, e_{j}} \equiv e_{i} e_{j} = e_{j} e_{i} = 2 I η_{i j}$ , where $I$ denotes the unit scalar of the algebra and ( $η_{i j}$ ) the nonsingular Minkowski...