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Annales Henri Poincaré, ISSN 1424-0637, 11/2016, Volume 17, Issue 11, pp. 3237 - 3254
Journal Article
Annals of Physics, ISSN 0003-4916, 03/2014, Volume 342, pp. 83 - 102
Journal Article
Annales Henri Poincaré, ISSN 1424-0637, 12/2013, Volume 14, Issue 8, pp. 2025 - 2043
Journal Article
The European Physical Journal C, ISSN 1434-6044, 8/2007, Volume 51, Issue 4, pp. 977 - 987
Journal Article
Pacific Journal of Mathematics, ISSN 0030-8730, 2015, Volume 173, Issue 1, pp. 169 - 195
We introduce Frechet quantum supergroups and their representations. By using the universal deformation formula of the abelian supergroups R-m vertical bar n we... 
Quantum group | Noncommutative supergeometry | Hopf algebra | Deformation quantization | Fréchet spaces | Multiplicative unitary | Frechet spaces | MATHEMATICS | quantum group | MULTIPLICATIVE UNITARIES | ALGEBRAS | deformation quantization | MANIFOLDS | noncommutative supergeometry | multiplicative unitary
Journal Article
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8121, 02/2011, Volume 44, Issue 5, pp. 055401 - 12
We investigate symmetries of the scalar field theory with a harmonic term on the Moyal space with the Euclidean scalar product and general symplectic form. The... 
DUALITY | ALGEBRAS | BETA-FUNCTION | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | RENORMALIZATION | Harmonics | Mathematical analysis | Scalars | Field theory | Orbits | Invariance | Invariants | Symmetry | Mathematics | Mathematical Physics | High Energy Physics - Theory | Physics
Journal Article
Journal of Physics: Conference Series, ISSN 1742-6588, 04/2015, Volume 597, Issue 1
This is a review of concepts of noncommutative supergeometry - namely Hilbert superspace, C*-superalgebra, quantum supergroup - and corresponding results. In... 
Conference Proceeding
Journal of Functional Analysis, ISSN 0022-1236, 08/2012, Volume 263, Issue 3, pp. 549 - 603
We construct a non-formal deformation machinery for the actions of the Heisenberg supergroup analogue to the one developed by M. Rieffel for the actions of Rd.... 
Graded operator algebras | Deformation quantization | Heisenberg supergroup | Fréchet functional spaces | Harmonic analysis | Supermanifolds | Renormalization | INDUCED GAUGE-THEORY | MATHEMATICS | SPACES | Frechet functional spaces | MANIFOLDS | Analysis | Algebra | Operator Algebras | Quantum Algebra | Mathematics | Differential Geometry | Mathematical Physics
Journal Article
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 2010, Volume 6, p. 048
The harmonic term in the scalar field theory on the Moyal space removes the UV-IR mixing, so that the theory is renormalizable to all orders. In this paper, we... 
Noncommutative QFT | Renormalization | Gauge theory | Heisenberg algebra | GAUGE-THEORY | ALGEBRAS | BETA-FUNCTION | renormalization | gauge theory | DUALITY | PARAMETRIC REPRESENTATION | PHYSICS, MATHEMATICAL | noncommutative QFT | Mathematics | Mathematical Physics | High Energy Physics - Theory | Physics
Journal Article
Advances in Mathematics, ISSN 0001-8708, 03/2016, Volume 291, pp. 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... 
Unitary representation | Orthogonality relation | Star-exponential | Deformation quantization | Bessel functions | Principal series | MATHEMATICS | ALGEBRA | Algebra
Journal Article
The European Physical Journal C, ISSN 1434-6044, 2/2008, Volume 53, Issue 3, pp. 459 - 466
Journal Article
Journal of Noncommutative Geometry, ISSN 1661-6952, 2012, Volume 6, Issue 2, pp. 343 - 387
Journal Article
International Mathematics Research Notices, ISSN 1073-7928, 08/2018
Journal Article
Journal of Physics: Conference Series, ISSN 1742-6596, 02/2008, Volume 103, Issue 1, p. 012010
J.Phys.Conf.Ser.103:012010,2008 We compute here the Yang-Mills effective action on Moyal space by integrating over the scalar fields in a noncommutative scalar... 
Journal Article
10/2014
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... 
Journal Article
05/2011
Pacific Journal of Mathematics 273 (2015) 169-195 In this paper, we introduce Fr\'echet quantum supergroups and their representations. By using the universal... 
Journal Article
01/2016
Numerous Lie supergroups do not admit superunitary representations except the trivial one, e.g., Heisenberg and orthosymplectic supergroups in mixed signature.... 
Journal Article
08/2011
Theta Ser. Adv. Math. 15 (2012) 61-73 We review recent works concerning deformation quantization of abelian supergroups. Indeed, we expose the construction of... 
Journal Article
11/2013
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... 
Journal Article
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