Bi-Gyrogroup: The Group-Like Structure Induced by Bi-Decomposition of Groups
نویسندگان
چکیده مقاله:
The decomposition $Gamma=BH$ of a group $Gamma$ into a subset B and a subgroup $H$ of $Gamma$ induces, under general conditions, a group-like structure for B, known as a gyrogroup. The famous concrete realization of a gyrogroup, which motivated the emergence of gyrogroups into the mainstream, is the space of all relativistically admissible velocities along with a binary mbox{operation} given by the Einstein velocity addition law of special relativity theory. The latter leads to the Lorentz transformation group $so{1,n}$, $ninN$, in pseudo-Euclidean spaces of signature $(1, n)$. The study in this article is motivated by generalized Lorentz groups $so{m, n}$, $m, ninN$, in pseudo-Euclidean spaces of signature $(m, n)$. Accordingly, this article explores the bi-decomposition $Gamma = H_LBH_R$ of a group $Gamma$ into a subset $B$ and subgroups $H_L$ and $H_R$ of $Gamma$, along with the novel bi-gyrogroup structure of $B$ induced by the bi-decomposition of $Gamma$. As an example, we show by methods of Clifford mbox{algebras} that the quotient group of the spin group $spin{m, n}$ possesses the bi-decomposition structure.
منابع مشابه
bi-gyrogroup: the group-like structure induced by bi-decomposition of groups
the decomposition $gamma=bh$ of a group $gamma$ into a subset $b$ and a subgroup $h$ of $gamma$ induces, under general conditions, a group-like structure for $b$, known as a gyrogroup. the famous concrete realization of a gyrogroup, which motivated the emergence of gyrogroups into the mainstream, is the space of all relativistically admissible velocities along with a binary operation given by t...
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عنوان ژورنال
دوره 1 شماره 1
صفحات 111- 142
تاریخ انتشار 2016-01-01
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