The n-ary algebra of tensors and of cubic and hypercubic matrices
| dc.creator | Goze, Nicolas | |
| dc.creator | Remm, Elisabeth | |
| dc.date | 2009-02-16 | |
| dc.date | 2009-03-10 | |
| dc.date.accessioned | 2026-07-07T12:50:14Z | |
| dc.date.available | 2026-07-07T12:50:14Z | |
| dc.description | We define a ternary product and more generally a (2k+1)-ary product on the vector space T^p_q(E) of tensors of type (p, q) that is contravariant of order p, covariant of order q and total order (p+q). This product is totally associative up to a permutation s_k of order k (we call this property a s_k-totally associativity). When p=2 and q=1, we obtain a (2k+1)-ary product on the space of bilinear maps on E with values on E, which is identified to the cubic matrices. Then we obtain a (2k+1)-ary product on the space of cubic matrices. If we call a l-matrix a square tableau with lx...xl entrances (if l=3 we have the cubic matrices and we speak about hypercubic matrices as soon as l >3), then the (2k+1)-ary product on T^p_q(E) gives a (2k+1)-product on the space of (p+q)-matrices. We describe also all these products which are s_k-totally associative. We compute the corresponding quadratic operads and their dual. | |
| dc.identifier | https://arxiv.org/abs/0902.2757 | |
| dc.identifier | http://arxiv.org/abs/0902.2757 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/222624 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Algebraic Topology | |
| dc.subject | 17A40; 18D50 | |
| dc.title | The n-ary algebra of tensors and of cubic and hypercubic matrices | |
| dc.type | text |