caa a22 4500 445813466 CHVBK 20180317145219.0 cr unu---uuuuu 170323e20110801xx s 000 0 eng 10.1007/s00022-011-0081-3 doi (NATIONALLICENCE)springer-10.1007/s00022-011-0081-3 Whitney algebras and Grassmann's regressive products [Elektronische Daten] [Andrea Brini, Francesco Regonati] Geometric products on tensor powers $${\Lambda(V)^{\otimes m}}$$ of an exterior algebra and on Whitney algebras (Crapo and Schmitt in J. Comb. Theory A 91:215-263, 2000) provide a rigorous version of Grassmann's regressive products of 1844 (Grassmann in Die Lineale Ausdehnungslehre, Verlag von Otto Wigand, Leipzig, 1844). We study geometric products and their relations with other classical operators on exterior algebras, such as the Hodge *−operators and the join and meet products in Cayley-Grassmann algebras (Barnabei etal. in J. Algebra 96:120-160, 1985; Stewart in Nature 321:17, 1986). We establish encodings of tensor powers $${\Lambda(V)^{\otimes m}}$$ and of Whitney algebras W m (M) in terms of letterplace algebras and of their geometric products in terms of divided powers of polarization operators. We use these encodings to provide simple proofs of the Crapo and Schmitt exchange relations in Whitney algebras and of two typical classes of identities in Cayley-Grassmann algebras. Springer Basel AG, 2011 Exterior algebra nationallicence Cayley-Grassmann algebra nationallicence Hopf algebra nationallicence Whitney algebra nationallicence polarization operator nationallicence straightening law nationallicence letterplace algebra nationallicence modular lattice nationallicence Brini Andrea Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato, 5, 40126, Bologna, Italy aut Regonati Francesco Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato, 5, 40126, Bologna, Italy aut Journal of Geometry SP Birkhäuser Verlag Basel 101/1-2(2011-08-01), 51-81 0047-2468 101:1-2<51 2011 101 22 https://doi.org/10.1007/s00022-011-0081-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00022-011-0081-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Brini Andrea Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato, 5, 40126, Bologna, Italy aut NATIONALLICENCE 700 1- Regonati Francesco Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato, 5, 40126, Bologna, Italy aut NATIONALLICENCE 773 0- Journal of Geometry SP Birkhäuser Verlag Basel 101/1-2(2011-08-01), 51-81 0047-2468 101:1-2<51 2011 101 22 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer