Homology of distributive lattices

Springer Science and Business Media LLC - Tập 8 Số 1 - Trang 35-65 - 2013
Józef H. Przytycki1, Krzysztof K. Putyra2
1Department of Mathematics, George Washington University, Washington, DC, 20052, USA
2Department of Mathematics, Columbia University, New York, NY 10027, USA

Tóm tắt

Từ khóa


Tài liệu tham khảo

Balbes R., Dwinger P.: Distributive Lattices. University of Missouri Press, Columbia (1974)

Bourbaki N.: Algebra I: Chapters 1–3, Elements of Mathematics. Springer, Berlin (1989)

Carter, J.S.: A Survey of Quandle Ideas, the chapter in the book Introductory Lectures on Knot Theory: Selected Lectures presented at the Advanced School and Conference on Knot Theory and its Applications to Physics and Biology, ICTP, Trieste, Italy, 11–29 May 2009. World Scientific, Series on Knots and Everything, vol. 46, pp. 22–53 (2011)

Carter S., Jelsovsky D., Kamada S., Langford L., Saito M.: State-sum invariants of knotted curves and surfaces from quandle cohomology. Electron. Res. Announc. Am. Math. Soc 5, 146–156 (1999)

Carter S., Jelsovsky D., Kamada S., Saito M.: Quandle homology groups, their Betti numbers, and virtual knots. J. Pure Appl. Algebra 157, 135–155 (2001)

Carter, S., Kamada, S., Saito, M.: Surfaces in 4-space. In: Gamkrelidze, R.V., Vassiliev, V.A. (eds.) Encyclopaedia of Mathematical Sciences, Low-Dimensional Topology III

Clauwens F.J.B.J.: The algebra of rack and quandle cohomology. J. Knot Theory Ramif. 20(11), 1487–1535 (2011)

Crans, A.S.: Lie 2-algebras. PhD dissertation (2004). UC Riverside, arXiv:math.QA/0409602

Etingof P., Grana M.: On rack cohomology. J. Pure Appl. Algebra 177, 49–59 (2003)

Frabetti, A.: Dialgebra (co)homology with coefficients. In: Loday, J.-L., Frabetti, A., Chapoton, F., Goichot, F. (eds.) Dialgebras and Related Operads. Lectures Notes in Mathematics, vol. 1763, pp. 67–103. Springer, Berlin (2001)

Frabetti A.: Dialgebra homology of associative algebras. C.R. Acad. Sci. Paris 325, 135–140 (1997)

Fenn, R.: Tackling the Trefoils (preprint, 2011); arXiv:1110.0582v1 (will appear in the volume “Virtual knots” in JKTR)

Fenn R., Rourke C.: Racks and links in codimension two. J. Knot Theory Ramif. 1(4), 343–406 (1992)

Fenn R., Rourke C., Sanderson B.J.: James bundles and applications. Proc. Lond. Math. Soc. 3(89(1), 217–240 (2004)

Grätzer, G.: Lattice Theory. First concepts and distributive lattices. W.H. Freeman, San Francisco (1971) (Dover edition 2009)

Greene, M.: Some results in geometric topology and geometry. PhD thesis, University of Warwick, advisor: Brian Sanderson (1997)

Hochschild G.: On the cohomology groups of an associative algebra. Ann. Math. 46, 58–67 (1945)

Inasaridze K.N.: Homotopy of pseudo-simplicial groups, nonabelian derived functors and algebraic K-theory. Math. USSR Sbornik 98(3), 339–362 (1975)

Joyce D.: A classifying invariant of knots: the knot quandle. J. Pure Appl. Algebra 23, 37–65 (1982)

Leech J.E.: Normal skew lattices. Semigroup Forum 44, 1–8 (1992)

Leech J.E.: Recent developments in the theory of skew lattices. Semigroup Forum 52, 7–24 (1996)

Leech J.E.: Skew lattices in rings. A. Universalis 26, 48–72 (1989)

Litherland R.A., Nelson S.: The Betti numbers of some finite racks. J. Pure Appl. Algebra 178, 187–202 (2003)

Loday, J.-L.: Cyclic Homology. Grund. Math. Wissen. Band 301. Springer, Berlin (1992) (second edition, 1998)

Niebrzydowski M., Przytycki J.H.: Burnside Kei. Fundamenta Mathematicae 190, 211–229 (2006)

Niebrzydowski M., Przytycki J.H.: Homology of dihedral quandles. J. Pure Appl. Algebra 213, 742–755 (2009)

Niebrzydowski M., Przytycki J.H.: The quandle of the trefoil as the dehn quandle of the torus. Osaka J. Math. 46(3), 645–659 (2009)

Niebrzydowski M., Przytycki J.H.: Homology operations on homology of quandles. J. Algebra 324, 1529–1548 (2010)

Niebrzydowski M., Przytycki J.H.: The second quandle homology of the Takasaki quandle of an odd abelian group is an exterior square of the group. J. Knot Theory Ramif. 20(1), 171–177 (2011)

T. Nosaka, On quandle homology groups of Alexander quandles of prime order. TAMS (submitted)

Ohtsuki T.: Quandles, in Problems on invariants of knots and 3-manifolds. Geom. Topol. Monogr. 4, 455–465 (2003)

Peirce C.S.: On the algebra of logic. Am. J. Math. 3(1), 15–57 (1880)

Przytycki J.H.: Distributivity versus associativity in the homology theory of algebraic structures. Demonstratio Math 44(4), 823–869 (2011)

Przytycki, J.H., Sikora, A.S.: Distributive products and their homology. Commun. Algebra (2012), arXiv:1105.3700v1

Serre, J.P.: Lie algebras and Lie groups, lectures given at Harvard University (1964), 2nd edn. Lecture Notes in Mathematics, vol. 1500, Springer, Berlin (1992)

Sikorski, R.: Boolean algebras. Springer, Berlin (1960) (second edition 1964)

Takasaki, M.: Abstraction of symmetric transformation (in Japanese). Tohoku Math. J. 49, 145–207 (1942/1943); the English translation is being prepared by S. Kamada

Tierney M., Vogel W.: Simplicial derived functors in “Category theory, homology theory and applications”. Springer LNM 68, 167–179 (1969)

Traczyk, T.: Wstçp do teorii algebr Boole’a, Biblioteka Matematyczna, Tom 37, PWN, Warszawa (1970)