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Relative Inversion and Embeddings

Relative Inversion and Embeddings Commencing from a monoidal semigroup 𝐴, we consider the geometry of the space 𝑊(𝐴) of pseudoregular elements. When 𝐴 is a Banachable algebra we show that there exist certain subspaces of 𝑊(𝐴) that can be realized as submanifolds of 𝐴. The space 𝑊(𝐴) contains certain subspaces constituting the Stiefel manifolds of framings for 𝐴. We establish several embedding results for such subspaces, where the relevant maps induce embeddings of associated Grassmann manifolds. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

Relative Inversion and Embeddings

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Publisher
de Gruyter
Copyright
© Heldermann Verlag
ISSN
1072-947X
eISSN
1072-9176
DOI
10.1515/GMJ.2004.425
Publisher site
See Article on Publisher Site

Abstract

Commencing from a monoidal semigroup 𝐴, we consider the geometry of the space 𝑊(𝐴) of pseudoregular elements. When 𝐴 is a Banachable algebra we show that there exist certain subspaces of 𝑊(𝐴) that can be realized as submanifolds of 𝐴. The space 𝑊(𝐴) contains certain subspaces constituting the Stiefel manifolds of framings for 𝐴. We establish several embedding results for such subspaces, where the relevant maps induce embeddings of associated Grassmann manifolds.

Journal

Georgian Mathematical Journal – de Gruyter

Published: Sep 1, 2004

Keywords: Banachable algebra; pseudoregular elements; relative inverse; rational retract; Stiefel manifold

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