期刊
ALGEBRA AND LOGIC
卷 -, 期 -, 页码 -出版社
SPRINGER
DOI: 10.1007/s10469-023-09716-z
关键词
singular superalgebra with switch; extended double; singular superalgebra with 2-dimensional even part
类别
It has been proven that a singular superalgebra with a 2-dimensional even part is isomorphic to a superalgebra B2|3(phi, xi, psi). Particularly, there are no infinite-dimensional simple singular superalgebras with a 2-dimensional even part. It has been shown that if a singular superalgebra contains an odd left annihilator, then it contains a nondegenerate switch. Lastly, it has been established that for any number N >= 5, except the numbers 6, 7, 8, 11, there exist singular superalgebras with a switch of dimension N. For the numbers N = 6, 7, 8, 11, there do not exist singular N-dimensional superalgebras with a switch.
It is proved that a singular superalgebra with a 2-dimensional even part is isomorphic to a superalgebra B2|3(phi, xi, psi). In particular, there do not exist infinite-dimensional simple singular superalgebras with a 2-dimensional even part. It is proved that if a singular superalgebra contains an odd left annihilator, then it contains a nondegenerate switch. Lastly, it is established that for any number N >= 5, except the numbers 6, 7, 8, 11, there exist singular superalgebras with a switch of dimension N. For the numbers N = 6, 7, 8, 11, there do not exist singular N -dimensional superalgebras with a switch.
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