Free product of operads and free basis of Lie-admissible operad
Bauyrzhan Sartayev
TL;DR
This paper defines the free product of operads, provides a method to find bases and dimensions, and proves the Lie-admissible operad is isomorphic to the free product of Lie and commutative operads.
Contribution
It introduces the concept of free product of operads and establishes a new isomorphism involving Lie-admissible operads.
Findings
Method for determining basis and dimension of free product operads
Lie-admissible operad is isomorphic to the free product of Lie and commutative operads
Provides foundational tools for operad algebra constructions
Abstract
In this paper, we introduce the definition of free product of operads, following the definition of a free product of algebras. There is a given method of finding the basis and dimension of the free product of operads. By anti-commutative operation, Lie-admissible algebra gives Lie algebra. We proved that Lie-admissible operad isomorphic to the free product of Lie and commutative(non-associative) operads.
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Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models