L-Algebras, Triplicial-Algebras, within an Equivalence of Categories Motivated by Graphs

DOI10.1080/00927872.2010.490540zbMath1237.05221arXiv0709.3453OpenAlexW2161827565MaRDI QIDQ3098159

Philippe Leroux

Publication date: 17 November 2011

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0709.3453

zbMATH Keywords

structure theoremsweighted directed graphseven trees\(NAP\)-algebrasCartier-Milnor-Mooregood triplesL-commutative algebrasMarkov L-coalgebrasplanar rooted symmetric ternary trees

Mathematics Subject Classification ID

Trees (05C05) Algebraic combinatorics (05E99) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Directed graphs (digraphs), tournaments (05C20) De Morgan algebras, ?ukasiewicz algebras (lattice-theoretic aspects) (06D30) Markov processes (60J99) Signed and weighted graphs (05C22) Nonassociative algebras satisfying other identities (17A30) Free nonassociative algebras (17A50) Bialgebras (16T10)

Related Items (7)

Tree series and pattern avoidance in syntax trees ⋮ Cliff operads: a hierarchy of operads on words ⋮ On the operad of bigraft algebras. ⋮ Lie and Jordan Products in Interchange Algebras ⋮ Duplicial algebras, parking functions, and Lagrange inversion ⋮ Dendriform Analogues of Lie and Jordan Triple Systems ⋮ Enveloping Operads and Bicolored Noncrossing Configurations

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