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THE COHOMOLOGY RING OF FREE LOOP SPACES 1. Introduction
THE COHOMOLOGY RING OF FREE LOOP SPACES 1. Introduction

... AW : S∗ (X×Y ) → S∗ (X)⊗S∗ (Y ) and EZ : S∗ (X)⊗S∗ (Y ) → S∗ (X×Y ) are reserved for the standard normalized Alexander-Whitney map and to the standard normalized Eilenberg-Zilber map concerning singular ...
Basics of associative algebras
Basics of associative algebras

... Of course, isomorphic as algebras means what you think it means. Formally, we say a homomorphism of F -algebras : A ! B is an F -linear map which also is a ring homomorphism. (Recall, since we are working in the category of unital rings, this means we need (1A ) = 1B .) Further, it is an isomorphism ...
full text (.pdf)
full text (.pdf)

ON QUADRATIC FORMS ISOTROPIC OVER THE FUNCTION
ON QUADRATIC FORMS ISOTROPIC OVER THE FUNCTION

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3.1 Quadratic Functions

... • Odd-degreed polynomials open up on one end and down on the other end. • WHY? (plug in large values for x and see!!) 12 Feb 2009 ...
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Dual Banach algebras

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part I: algebra - Waterloo Computer Graphics Lab

nearly associative - American Mathematical Society
nearly associative - American Mathematical Society

... One verifies easily that if the subscripts here are interpreted modulo 7, every possible product of basis elements is defined exactly once by these equations. It is also clear that for each value of i the elements 1, ei9 ei+l9 ei+3 span a subalgebra which is isomorphic to the quaternions. Once the o ...
Frobenius algebras and monoidal categories
Frobenius algebras and monoidal categories

... bicategories. In Vect k - Mod the pseudomonoids include monoidal k-linear categories such as Vect k itself. The Frobenius requirement is related to the notion of star-autonomy due to Michael Barr. Every rigid (autonomous, compact) monoidal category is star-autonomous. In particular, Vect k is Froben ...
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Here - Mathematisches Institut der Universität Bonn

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Contents Lattices and Quasialgebras Helena Albuquerque 5

splitting in relation algebras - American Mathematical Society
splitting in relation algebras - American Mathematical Society

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- Lancaster EPrints

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Graduate lectures on operads and topological field theories

... the m-valent part of S is associated with m-valent vertices of Γ. We then take the tensor product of these tensors over all vertices of Γ and contract along the edges using the inverse of the given scalar product. These inverses are called propagators in physics. The resulting number is the Feynman ...
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... children play a form of hopscotch called Jumby. The pattern for this game is shown at the right. ...
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Topology Change for Fuzzy Physics: Fuzzy Spaces as Hopf Algebras

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Quantum Symmetries and K-Theory
Quantum Symmetries and K-Theory

... When there is a homomorphism of group extensions based on ψ : G2 → G1 such that ϕ ◦ ψ and ψ ◦ ϕ are the identity then the group extensions are said to be isomorphic extensions. Given group N and Q it can certainly happen that there is more than one nonisomorphic extension of Q by N . Classifying all ...
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... Given a vector field V(p) on a manifold M, we have seen how we can (at least locally) produce integral curves of V using the vector exponential map. Each point p in the neighborhood of interest lies on exactly one such curve, and the velocity of the curve at that point is exactly the vector given by ...
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Clifford algebra

In mathematics, Clifford algebras are a type of associative algebra. As K-algebras, they generalize the real numbers, complex numbers, quaternions and several other hypercomplex number systems. The theory of Clifford algebras is intimately connected with the theory of quadratic forms and orthogonal transformations. Clifford algebras have important applications in a variety of fields including geometry, theoretical physics and digital image processing. They are named after the English geometer William Kingdon Clifford.The most familiar Clifford algebra, or orthogonal Clifford algebra, is also referred to as Riemannian Clifford algebra.
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