Constructs left adjoint to restriction functor between categories of reductive Lie algebra pairs and Lie-Yamaguti algebras; enveloping algebra becomes right adjoint under surjective morphisms.
Yamaguti algebras and noncrossing partitions
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abstract
Recently, Das defined a new type of algebras, the Yamaguti algebras, which are supposed to serve as envelopes of Lie-Yamaguti algebras appearing naturally in differential geometry. We show that the nonsymmetric operad of Yamaguti algebras admit a simple combinatorial description via noncrossing partitions without singleton blocks.
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Free Reductive Lie Algebra Pairs of Lie-Yamaguti algebras
Constructs left adjoint to restriction functor between categories of reductive Lie algebra pairs and Lie-Yamaguti algebras; enveloping algebra becomes right adjoint under surjective morphisms.