Gröbner-Shirshov basis for Lie algebras
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Abstract (EN)
Denote by Lie(X) and L(2)(X) the free Lie algebras and free metabelian Lie algebras generated by X respectively. In this thesis, associative Lyndon-Shirshov words (ALSW) and non-associative Lyndon-Shirshov words (NLSW) are defined and for ALSW's two bracketing ways are introduced. A comprehensive proof Shirshov's Composition-Diamond Lemma for Lie(X) is given by using properties of these words. In addition, seven different types of compositions are introduced for free metabelian Lie algebras and for L(2)(X) Gröbner-Shirshov basis is obtained by using these compositions. As its applications Gröbner-Shirshov basis for free metabelian Lie product and partial commutative metabelian Lie algebras related to some graph (Circ_n circuit, Γ tree and Cu_3) are given.
Author
Merve Tuğçe Kalay
How to Cite
Merve Tuğçe Kalay (Master Thesis). Gröbner-Shirshov basis for Lie algebras, 2019, Osmaniye Korkut Ata University.
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