| 书目名称 | Smooth Quasigroups and Loops | | 编辑 | Lev V. Sabinin | | 视频video | | | 丛书名称 | Mathematics and Its Applications | | 图书封面 |  | | 描述 | 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 purel | | 出版日期 | Book 1999 | | 关键词 | Algebraic structure; Group theory; Volume; algebra; differential geometry | | 版次 | 1 | | doi | https://doi.org/10.1007/978-94-011-4491-9 | | isbn_softcover | 978-94-010-5921-3 | | isbn_ebook | 978-94-011-4491-9 | | copyright | Springer Science+Business Media Dordrecht 1999 |
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发表于 2025-3-21 16:46:58
