Smooth Quasigroups and Loops:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1999
|
| Schriftenreihe: | Mathematics and Its Applications
492 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | During the last twenty-five years quite remarkable relations between nonas sociative algebra and differential geometry have been discovered in our work. Such exotic structures of algebra as quasigroups and loops were obtained from purely geometric structures such as affinely connected spaces. The notion ofodule was introduced as a fundamental algebraic invariant of differential geometry. For any space with an affine connection loopuscular, odular and geoodular structures (partial smooth algebras of a special kind) were introduced and studied. As it happened, the natural geoodular structure of an affinely connected space al lows us to reconstruct this space in a unique way. Moreover, any smooth ab stractly given geoodular structure generates in a unique manner an affinely con nected space with the natural geoodular structure isomorphic to the initial one. The above said means that any affinely connected (in particular, Riemannian) space can be treated as a purely algebraic structure equipped with smoothness. Numerous habitual geometric properties may be expressed in the language of geoodular structures by means of algebraic identities, etc.. Our treatment has led us to the purely algebraic concept of affinely connected (in particular, Riemannian) spaces; for example, one can consider a discrete, or, even, finite space with affine connection (in the form ofgeoodular structure) which can be used in the old problem of discrete space-time in relativity, essential for the quantum space-time theory |
| Beschreibung: | 1 Online-Ressource (XVI, 249 p) |
| ISBN: | 9789401144919 9789401059213 |
| DOI: | 10.1007/978-94-011-4491-9 |
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| 500 | |a During the last twenty-five years quite remarkable relations between nonas sociative algebra and differential geometry have been discovered in our work. Such exotic structures of algebra as quasigroups and loops were obtained from purely geometric structures such as affinely connected spaces. The notion ofodule was introduced as a fundamental algebraic invariant of differential geometry. For any space with an affine connection loopuscular, odular and geoodular structures (partial smooth algebras of a special kind) were introduced and studied. As it happened, the natural geoodular structure of an affinely connected space al lows us to reconstruct this space in a unique way. Moreover, any smooth ab stractly given geoodular structure generates in a unique manner an affinely con nected space with the natural geoodular structure isomorphic to the initial one. The above said means that any affinely connected (in particular, Riemannian) space can be treated as a purely algebraic structure equipped with smoothness. Numerous habitual geometric properties may be expressed in the language of geoodular structures by means of algebraic identities, etc.. Our treatment has led us to the purely algebraic concept of affinely connected (in particular, Riemannian) spaces; for example, one can consider a discrete, or, even, finite space with affine connection (in the form ofgeoodular structure) which can be used in the old problem of discrete space-time in relativity, essential for the quantum space-time theory | ||
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Datensatz im Suchindex
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-011-4491-9 |
| format | Electronic eBook |
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| id | DE-604.BV042423943 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:14Z |
| institution | BVB |
| isbn | 9789401144919 9789401059213 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027859360 |
| oclc_num | 863687234 |
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| physical | 1 Online-Ressource (XVI, 249 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1999 |
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| publisher | Springer Netherlands |
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| series2 | Mathematics and Its Applications |
| spelling | Sabinin, Lev V. Verfasser aut Smooth Quasigroups and Loops by Lev V. Sabinin Dordrecht Springer Netherlands 1999 1 Online-Ressource (XVI, 249 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 492 During the last twenty-five years quite remarkable relations between nonas sociative algebra and differential geometry have been discovered in our work. Such exotic structures of algebra as quasigroups and loops were obtained from purely geometric structures such as affinely connected spaces. The notion ofodule was introduced as a fundamental algebraic invariant of differential geometry. For any space with an affine connection loopuscular, odular and geoodular structures (partial smooth algebras of a special kind) were introduced and studied. As it happened, the natural geoodular structure of an affinely connected space al lows us to reconstruct this space in a unique way. Moreover, any smooth ab stractly given geoodular structure generates in a unique manner an affinely con nected space with the natural geoodular structure isomorphic to the initial one. The above said means that any affinely connected (in particular, Riemannian) space can be treated as a purely algebraic structure equipped with smoothness. Numerous habitual geometric properties may be expressed in the language of geoodular structures by means of algebraic identities, etc.. Our treatment has led us to the purely algebraic concept of affinely connected (in particular, Riemannian) spaces; for example, one can consider a discrete, or, even, finite space with affine connection (in the form ofgeoodular structure) which can be used in the old problem of discrete space-time in relativity, essential for the quantum space-time theory Mathematics Group theory Geometry Global differential geometry Number theory Group Theory and Generalizations Differential Geometry Number Theory Applications of Mathematics Mathematik https://doi.org/10.1007/978-94-011-4491-9 Verlag Volltext |
| spellingShingle | Sabinin, Lev V. Smooth Quasigroups and Loops Mathematics Group theory Geometry Global differential geometry Number theory Group Theory and Generalizations Differential Geometry Number Theory Applications of Mathematics Mathematik |
| title | Smooth Quasigroups and Loops |
| title_auth | Smooth Quasigroups and Loops |
| title_exact_search | Smooth Quasigroups and Loops |
| title_full | Smooth Quasigroups and Loops by Lev V. Sabinin |
| title_fullStr | Smooth Quasigroups and Loops by Lev V. Sabinin |
| title_full_unstemmed | Smooth Quasigroups and Loops by Lev V. Sabinin |
| title_short | Smooth Quasigroups and Loops |
| title_sort | smooth quasigroups and loops |
| topic | Mathematics Group theory Geometry Global differential geometry Number theory Group Theory and Generalizations Differential Geometry Number Theory Applications of Mathematics Mathematik |
| topic_facet | Mathematics Group theory Geometry Global differential geometry Number theory Group Theory and Generalizations Differential Geometry Number Theory Applications of Mathematics Mathematik |
| url | https://doi.org/10.1007/978-94-011-4491-9 |
| work_keys_str_mv | AT sabininlevv smoothquasigroupsandloops |