On analogs of some classical group-theoretic results in Poisson algebras
2021 ◽
pp. 11-16
Keyword(s):
We investigate the Poisson algebras, in which the n-th hypercenter (center) has a finite codimension. It was established that, in this case, the Poisson algebra P includes a finite-dimensional ideal K such that P/K is nilpotent (Abelian). Moreover, if the n-th hypercenter of a Poisson algebra P over some field has a finite codimension, and if P does not contain zero divisors, then P is Abelian.
Keyword(s):
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1990 ◽
Vol 120
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pp. 113-127
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1982 ◽
Vol 91
(3-4)
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pp. 243-263
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2014 ◽
Vol 14
(2)
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pp. 371-386
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2001 ◽
Vol 29
(10)
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pp. 4655-4669
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2011 ◽
Vol 369
(1939)
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pp. 1264-1279
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