Sets with two associative operations

• Autorzy: Teimuraz Pirashvili
• Języki publikacji: EN

Abstrakty

EN

In this paper we consider duplexes, which are sets with two associative binary operations. Dimonoids in the sense of Loday are examples of duplexes. The set of all permutations carries a structure of a duplex. Our main result asserts that it is a free duplex with an explicitly described set of generators. The proof uses a construction of the free duplex with one generator by planary trees.

Słowa kluczowe

EN

Trees; permutations; free algebras; 05E99; 20M05; 08B20

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2003
• Tom: 1
• Numer: 2
• Strony: 169-183

Daty

wydano

2003-06-01

online

2003-06-01

Twórcy

autor

Teimuraz Pirashvili

• A.M. Razmadze Mathematical Inst.

Bibliografia

• [1] M. Aguiar and F. Sottile: Structures of the Malvenuto-Reutenauer Hopf algebra of permutations, Preprint (2002), http://front.math.ucdavis.edu/math.CO/0203282.
• [2] J.-L. Loday: “Algébras ayant deux opérations associatives (digébres)”, C. R. Acad. Sci. Paris Sér. I Math., Vol. 321, (1995), pp. 141–146.
• [3] J.-L. Loday: “Dialgebras”, In: Dialgebras and related operads, Lecture Notes in Math. 1763, Springer, Berlin, 2001, pp. 7–66.
• [4] J.-L. Loday: “Arithmetree”, J. of Algebra, Vol. 258, (2002), pp. 275–309. http://dx.doi.org/10.1016/S0021-8693(02)00510-0
• [5] J.-L. Loday and M. O. Ronco: “Order structure on the algebra of permutations and of planar binary trees”, J. Algebraic Combin., Vol. 15, (2002), pp. 253–270 http://dx.doi.org/10.1023/A:1015064508594
• [6] J.-L. Loday and M. O. Ronco: Trialgebras and families of polytopes, Preprint (2002), http://front.math.ucdavis.edu/math.AT/0205043.
• [7] B. Richter: Dialgebren, Doppelalgebren und ihre Homologie, Diplomarbeit, Universität Bonn, 1997, http://www.math.uni-bonn.de/people/richter/.

Identyfikatory

DOI

10.2478/BF02476006