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Exterior Tensor Powers and Exterior Algebras
2020In this chapter we consider alternating (also called skew-symmetric) multilinear maps and exterior tensor powers (also called alternating tensor powers), denoted \(\bigwedge ^n(E)\). In many respects alternating multilinear maps and exterior tensor powers can be treated much like symmetric tensor powers, except that sgn(σ) needs to be inserted in front
Jean Gallier, Jocelyn Quaintance
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The Exterior Product and Exterior Algebras
2012The chapter begins with notion of the Plucker coordinates of a subspace in a vector space. Then the Plucker relations are derived, and the Grassmann varieties are described. Then an exterior product of vectors is defined, and the connection between the exterior product and Plucker coordinates is explained: the Plucker relations give necessary and ...
Igor R. Shafarevich, Alexey O. Remizov
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Exteriorized colonic anastomosis
International Journal of Colorectal Disease, 1991The risk of anastomotic failure in the unprepared colon is generally high. Therefore, Hartmann's operation is frequently employed in emergencies. We present an alternative technique, the exteriorized anastomosis described until now only for cases of perforation. Exteriorized anastomosis was performed in 14 patients.
M, Alonso Cohen +6 more
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On the Tubes of Exterior Algebras
Algebra Colloquium, 2006In this paper, we study the Koszul modules of complexity 1 of an exterior algebra of a vector space V over an algebraically closed field. We prove that there are ℙ (V)-orthogonal families of such modules, each of which consists of Koszul modules filtered by the cyclic ones corresponding to the same point in ℙ (V). We also prove that they are invariant
Guo, Jinyun, Wu, Qiuxian, Wan, Qianhong
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A note on the exterior centralizer
Archiv der Mathematik, 2009If \(G\) is a group, the exterior square of \(G\) is the group \(G\wedge G\) generated by the symbols \(g\wedge h\) and subject to the relations \(g\wedge g=1\), \(g_1g_2\wedge h=(g_1g_2g_1^{-1}\wedge g_1hg_1^{-1})(g_1\wedge h)\) and \(g\wedge h_1h_2=(g\wedge h_1)(h_1gh_1^{-1}\wedge h_1h_2h_1^{-1})\) for all \(g,g_1,g_2,h,h_1,h_2\in G\).
Niroomand, P, RUSSO, Francesco
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A Homomorphism in Exterior Algebra
Canadian Journal of Mathematics, 1964In the following, V is a vector space over an arbitrary field F, dimFV = n. Let {e1, . . . , en} be a basis for V, and {f1, . . . , fn} be the dual basis for and , then the operators *(u) and i(g) (exterior and inner multiplication by u and g respectively) set up an equivalence between the ideal = range of ∊(u) and the sub-algebra = range of i(g ...
Kostant, Bertram, Novikoff, A.
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On the exterior structure of graphs
Journal of Mathematical Physics, 2004After a detailed ab initio description of the exterior structure of graphs as handled by Connes and Kreimer in their work on renormalization (illustrated by the example of the φ3 model in six dimensions) we spell out in detail their study of the Lie algebra of infinitesimal characters and of the group of characters of the Hopf algebra of Feynman graphs.
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Exterior Topology and Revision Spaces
Journal of Logic and Computation, 1995Summary: A mathematical model of knowledge base revision attempts to faithfully capture an intuitive notion of `closest' new information relative to some given background information. An attempt to topologically characterize this notion of closest information leads naturally to an approach using non-monotonic exterior operators in contrast to standard ...
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