Deformations of the Galilean algebra
Deformations of the Galilean algebra
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伽利略代数的变形
DOI：
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发表时间：
1989
期刊：
影响因子：
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通讯作者：
J. Figueroa
中科院分区：
文献类型：
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作者：
J. Figueroa
计算了有中心扩张和无中心扩张的伽利略代数的所有无穷小变形及其可积性。在未扩张代数的无穷小变形的四参数族中，可以找到牛顿代数、欧几里得代数E（4）、庞加莱代数、德西特代数和SO（5）。对于中心扩展代数有发现，特别是，一个无穷小变形包含庞加莱子代数（虽然嵌入不是自然的），和中心扩展版本的牛顿代数。
All the infinitesimal deformations of the Galilean algebra with and without central extension are computed, as well as their integrability properties. Among the four‐parameter family of infinitesimal deformations of the unextended algebra is found the Newton algebras, the Euclidean algebra E(4), the Poincare algebra, the de Sitter algebras, and SO(5). For the centrally extended algebra there is found, in particular, an infinitesimal deformation containing a Poincare subalgebra (although the embedding is not the natural one), and centrally extended versions of the Newton algebras.