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Distributive laws between the operads Lie and Com. (English) Zbl 07276752
MSC:
18M60 Operads (general)
13C10 Projective and free modules and ideals in commutative rings
13N15 Derivations and commutative rings
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
15A54 Matrices over function rings in one or more variables
15A69 Multilinear algebra, tensor calculus
16S37 Quadratic and Koszul algebras
17A30 Nonassociative algebras satisfying other identities
17A50 Free nonassociative algebras
17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.)
17B63 Poisson algebras
68W30 Symbolic computation and algebraic computation
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References:
[1] Y.-H. Bao, Y.-H. Wang, X.-W. Xu, Y. Ye, J. J. Zhang and Z.-B. Zhao, Cohomological invariants of algebraic operads, I, arXiv preprint https://arXiv.org/abs/2001.05098, 2020.
[2] J. Beck, Distributive laws, Seminar on Triples and Categorical Homology Theory (ETH, Zürich, 1966/67), Lecture Notes in Mathematics, Vol. 80, eds. B. Eckmann and M. Tierney (Springer-Verlag, Berlin-Heidelberg, 1969), Republished in: Reprints in Theory Appl. Categ. 18 (2008) 1-303, www.tac.mta.ca/tac/reprints/articles/18/tr18.pdf.
[3] Bremner, M. and Dotsenko, V., Algebraic Operads: An Algorithmic Companion (Chapman and Hall/CRC, Boca Raton, FL, USA, 2016). · Zbl 1350.18001
[4] Bremner, M. and Dotsenko, V., Classification of regular parametrised one-relation operads, Canadian J. Math.69(5) (2017) 992-1035. · Zbl 1388.18010
[5] M. Bremner and V. Dotsenko, Distributive laws between the operads Lie and Com: Extended abstract, Maple in Mathematics Education and Research. Third Maple Conference, MC 2019, Waterloo, Ontario, Canada, October 15-17, 2019, Proceedings. Communications in Computer and Information Science (Springer International Publishing AG, Cham, Switzerland, 2020), pp. xi+363.
[6] Bremner, M. and Markl, M., Distributive laws between the three graces, Theory Appl. Categ.34(41) (2019) 1317-1342. · Zbl 1448.18029
[7] Dotsenko, V. and Griffin, J., Cacti and filtered distributive laws, Algebr. Geom. Topol.14(6) (2014) 3185-3225. · Zbl 1305.18033
[8] Dotsenko, V. and Tamaroff, P., Endofunctors and Poincaré-Birkhoff-Witt theorems, Int. Math. Res. Not.Article ID rnz369, 2020, 21 pp.
[9] Loday, J.-L. and Vallette, B., Algebraic Operads, , Vol. 346 (Springer, Heidelberg, Germany, 2012), pp. xxiv+634. · Zbl 1260.18001
[10] Macdonald, I. G., Symmetric functions and Hall polynomials, Oxford Classic Texts in the Physical Sciences (The Clarendon Press, Oxford University Press, New York, 2015), pp. xii+475. · Zbl 1332.05002
[11] Markl, M., Distributive laws and Koszulness, Ann. Inst. Fourier (Grenoble)46(2) (1996) 307-323. · Zbl 0853.18005
[12] Markl, M. and Remm, E., Algebras with one operation including Poisson and other Lie-admissible algebras, J. Algebra299(1) (2006) 171-189. · Zbl 1101.18004
[13] Polishchuk, A. and Positselski, L., Quadratic Algebras, , Vol. 37 (American Mathematical Society, Providence, RI, 2005). · Zbl 1145.16009
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