Bilinear forms and 2-dimensional cohomology
نویسندگان
چکیده
منابع مشابه
Bilinear Forms
The geometry of Rn is controlled algebraically by the dot product. We will abstract the dot product on Rn to a bilinear form on a vector space and study algebraic and geometric notions related to bilinear forms (especially the concept of orthogonality in all its manifestations: orthogonal vectors, orthogonal subspaces, and orthogonal bases). Section 1 defines a bilinear form on a vector space a...
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Assume that $A$, $B$ are Banach algebras and that $m:Atimes Brightarrow B$, $m^prime:Atimes Arightarrow B$ are bounded bilinear mappings. We study the relationships between Arens regularity of $m$, $m^prime$ and the Banach algebras $A$, $B$. For a Banach $A$-bimodule $B$, we show that $B$ factors with respect to $A$ if and only if $B^{**}$ is unital as an $A^{**}$-module. Le...
متن کاملDifferential Forms and Cohomology
Definition 1. An m-linear function f which maps the m-fold cartesian product V m of a vector space V into some other vector space W is called alternating if f(v1, . . . , vm) = 0 whenever v1, . . . , vm ∈ V and vi = vj for i 6= j. We let ∧ (V ,W ) be the vector space of mlinear alternating functions mapping V m intoW . We then define ∧m V by the property that if f ∈ ∧m(V,W ) then there exists a...
متن کاملOn continuous cohomology of locally compact Abelian groups and bilinear maps
Let $A$ be an abelian topological group and $B$ a trivial topological $A$-module. In this paper we define the second bilinear cohomology with a trivial coefficient. We show that every abelian group can be embedded in a central extension of abelian groups with bilinear cocycle. Also we show that in the category of locally compact abelian groups a central extension with a continuous section can b...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
سال: 1986
ISSN: 0263-6115
DOI: 10.1017/s1446788700033589