Hopf-like Algebras and Extended P-B-W Theorems

Mathematics – Rings and Algebras

Scientific paper

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12 pages

Scientific paper

Based on invariant algebras, we introduce representations$^{6-th}$ of Lie
algebras and representations$^{< 4-th>}$ of Leibniz algebras, give the extended
P-B-W Theorems in the context of the new representations of Lie algebras and
Leibniz algebras, and generalize the Hopf-algebra structure on the enveloping
algebras of Lie Algebras.

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