Algebra Versus Its Anti-symmetric Algebra
For a given algebra A= 〈A,+,·〉, we can define its anti-symmetric algebra A-= 〈A-,+,[ , ]〉 using the commutator [ , ] of A, where the sets A and A- are the same. We show that there are isomorphic algebras A1 and A2 such that their anti-symmetric algebras are not isomorphic. We define a special type Lie algebra and show that it is simple.
2016 ◽
Vol 15
(03)
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pp. 1650049
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2019 ◽
Vol 62
(3)
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pp. 875-887
Keyword(s):
1996 ◽
Vol 120
(2)
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pp. 193-206