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ORBi

A tale of three homotopies ; Poncin, Norbert E-print/Working paper (2012) Detailed reference viewed: 77 (13 UL)Lectures on Supergeometry Covolo, Tiffany ; Poncin, Norbert E-print/Working paper (2012) Detailed reference viewed: 566 (170 UL)Graded Algebra and Geometry Covolo, Tiffany ; ; Poncin, Norbert Report (2012) Abstracts and list of participants of the Workshop on "Graded Algebra and Geometry" organized in December 2012 at the University of Luxembourg by Tiffany Covolo, Valentin Ovsienko, and Norbert Poncin Detailed reference viewed: 162 (9 UL)Higher trace and Berezinian of matrices over a Clifford algebra Covolo, Tiffany ; ; Poncin, Norbert in Journal of Geometry and Physics (2012), 62(11), 22942319 We define the notions of trace, determinant and, more generally, Berezinian of matrices over a (Z_2)^n-graded commutative associative algebra A. The applications include a new approach to the classical ... [more ▼] We define the notions of trace, determinant and, more generally, Berezinian of matrices over a (Z_2)^n-graded commutative associative algebra A. The applications include a new approach to the classical theory of matrices with coefficients in a Clifford algebra, in particular of quaternionic matrices. In a special case, we recover the classical Dieudonné determinant of quaternionic matrices, but in general our quaternionic determinant is different. We show that the graded determinant of purely even (Z_2)^n-graded matrices of degree 0 is polynomial in its entries. In the case of the algebra A = H of quaternions, we calculate the formula for the Berezinian in terms of a product of quasiminors in the sense of Gelfand, Retakh, and Wilson. The graded trace is related to the graded Berezinian (and determinant) by a (Z_2)^n-graded version of Liouville’s formula. [less ▲] Detailed reference viewed: 249 (55 UL)Fiber bundles and connections Poncin, Norbert ; ; et al E-print/Working paper (2012) Detailed reference viewed: 220 (29 UL)Higher categorified algebras versus bounded homotopy algebras Khudaverdyan, David ; ; Poncin, Norbert in Theory and Applications of Categories (2011), 25 Detailed reference viewed: 114 (17 UL)Geometric structures encoded in the Lie structure of an Atiyah algebroid ; ; Poncin, Norbert in Transformation Groups (2011), 16(1), 137--160 Detailed reference viewed: 175 (3 UL)Higher Loday Algebras Poncin, Norbert Scientific Conference (2011) Detailed reference viewed: 95 (16 UL)Lectures on Algebraic Operads ; Poncin, Norbert E-print/Working paper (2011) Detailed reference viewed: 217 (22 UL)Geometry of Manifolds and Mathematical Physics Poncin, Norbert Report (2011) Detailed reference viewed: 124 (7 UL)Coalgebraic approach to the Loday infinity category, stem differential for 2n-ary graded and homotopy algebras Ammar, Mourad ; Poncin, Norbert in Annales de l'Institut Fourier (2010), 60(1), 355--387 Detailed reference viewed: 148 (13 UL)Equivariant quantization of orbifolds Poncin, Norbert ; ; in Journal of Geometry and Physics (2010), 60(9), 1103--1111 Detailed reference viewed: 165 (3 UL)The Lie superalgebra of a supermanifold ; ; Poncin, Norbert in Journal of Lie Theory (2010), 20(4), 739--749 Detailed reference viewed: 120 (7 UL)Strongly r-matrix induced tensors, Koszul cohomology and arbitrary-dimensional quadratic Poisson cohomology Ammar, Mourad ; ; et al in Pacific Journal of Mathematics (2010), 245(1), 1--23 Detailed reference viewed: 172 (5 UL)Higher categorified algebras versus truncated homotopy algebras Poncin, Norbert Presentation (2010) Detailed reference viewed: 78 (3 UL)Equivariant quantization of orbifolds Poncin, Norbert Scientific Conference (2010) Detailed reference viewed: 144 (9 UL)A first approximation for quantization of singular spaces Poncin, Norbert ; ; in Journal of Geometry and Physics (2009), 59(4), 503--518 Detailed reference viewed: 184 (4 UL)Théorie des représentations du groupe symétrique ; Poncin, Norbert E-print/Working paper (2009) Detailed reference viewed: 92 (5 UL) |
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