Zobrazeno 1 - 10
of 110
pro vyhledávání: '"de Goursac, A."'
Numerous Lie supergroups do not admit superunitary representations except the trivial one, e.g., Heisenberg and orthosymplectic supergroups in mixed signature. To avoid this situation, we introduce in this paper a broader definition of superunitary r
Externí odkaz:
http://arxiv.org/abs/1601.07387
Autor:
de Goursac, Axel
This is a review of concepts of noncommutative supergeometry - namely Hilbert superspace, C*-superalgebra, quantum supergroup - and corresponding results. In particular, we present applications of noncommutative supergeometry in harmonic analysis of
Externí odkaz:
http://arxiv.org/abs/1501.06316
Publikováno v:
Advances in Mathematics 291 (2016) 362-402
In this paper, we exhibit the non-formal star-exponential of the Lie group SL(2,R) realized geometrically on the curvature contraction of its one-sheeted hyperboloid orbits endowed with its natural non-formal star-product. It is done by a direct reso
Externí odkaz:
http://arxiv.org/abs/1501.07491
Publikováno v:
Ann. Henri Poincar\'e (2016) 17: 3237-3254
The Jacobian Conjecture states that any locally invertible polynomial system in C^n is globally invertible with polynomial inverse. C. W. Bass et al. (1982) proved a reduction theorem stating that the conjecture is true for any degree of the polynomi
Externí odkaz:
http://arxiv.org/abs/1411.6558
Autor:
de Goursac, Axel
In this paper, we introduce the notion of multiplier of a Hilbert algebra. The space of bounded multipliers is a semifinite von Neumann algebra isomorphic to the left von Neumann algebra of the Hilbert algebra, as expected. However, in the unbounded
Externí odkaz:
http://arxiv.org/abs/1410.3434
Publikováno v:
Geom. Methods Phys. XXXI Workshop Bialowieza (2012) 3-12, Trends in Mathematics
We recall the construction of non-formal deformation quantization of the Poincare Group ISO(1,1) on its coadjoint orbit and exhibit the associated non-formal star-exponentials.
Comment: 10 pages, Proceedings of the conference "XXXI Workshop on G
Comment: 10 pages, Proceedings of the conference "XXXI Workshop on G
Externí odkaz:
http://arxiv.org/abs/1311.2339
Publikováno v:
Dev. Math. 37 (2014) 41-76, Springer
We define and study a noncommutative Fourier transform on every homogeneous complex bounded domain. We then give an application in noncommutative differential geometry by defining noncommutative Baumslag-Solitar tori.
Comment: 27 pages
Comment: 27 pages
Externí odkaz:
http://arxiv.org/abs/1311.1871
Publikováno v:
Ann. Phys. 342: 83-102, 2014
We construct a version of the complex Heisenberg algebra based on the idea of endless analytic continuation. In particular, we exhibit an integral formula for the product of resurgent operators with algebraic singularities. This algebra would be larg
Externí odkaz:
http://arxiv.org/abs/1309.0437
Autor:
de Goursac, Axel
Publikováno v:
Annales Henri Poincare 14 (2013) 2025-2043
The noncommutative scalar theory with harmonic term (on the Moyal space) has a vanishing beta function. In this paper, we prove the renormalizability of the commutative scalar field theory with harmonic term to all orders by using multiscale analysis
Externí odkaz:
http://arxiv.org/abs/1207.6208
Autor:
de Goursac, Axel
Publikováno v:
Theta Ser. Adv. Math. 15 (2012) 61-73
We review recent works concerning deformation quantization of abelian supergroups. Indeed, we expose the construction of an induced representation of the Heisenberg supergroup and an associated pseudodifferential calculus by using Kirillov's orbits m
Externí odkaz:
http://arxiv.org/abs/1108.3947