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Algebraic properties of gyrogroups |
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| รหัสดีโอไอ | |
| Title | Algebraic properties of gyrogroups |
| Creator | Teerapong Suksumran |
| Contributor | Keng Wiboonton |
| Publisher | Chulalongkorn University |
| Publication Year | 2558 |
| Keyword | Algebra, พีชคณิต |
| Abstract | In the first part of the dissertation, we give an algebraic proof that the open unit ball B of Euclidean space Rn, equipped with Einstein addition E, forms a uniquely 2-divisible gyrocommutative gyrogroup or, equivalently, a B-loop, using the Clifford algebra formalism. As a consequence, we obtain a compact formula for Einstein addition in terms of Möbius addition. We then give a characterization of associativity and commutativity of vectors in with respect to Einstein addition. In the second part of the dissertation, we study gyrogroups from an algebraic point of view. We extend some well-known theorems in group theory to gyrogroups, including Cayley’s theorem, the isomorphism theorems, and Lagrange’s theorem. We also prove that gyro-groups of particular order satisfy the Cauchy property. |
| URL Website | cuir.car.chula.ac.th |
