TY - JOUR T1 - Yang-Baxter Equation in Lattice Effect Algebras AU - Öner, Tahsin AU - Kalkan, Tuğçe AU - Ülker, Alper PY - 2020 DA - April Y2 - 2020 JF - Konuralp Journal of Mathematics JO - Konuralp J. Math. PB - Mehmet Zeki SARIKAYA WT - DergiPark SN - 2147-625X SP - 106 EP - 113 VL - 8 IS - 1 LA - en AB - In this paper, we present lattice effect algebra by giving certain definitions and conceptions as to lattice effect algebra. We present newsolutions to the set-theoratical Yang-Baxter equation by using lattice effect algebras. KW - Yang–Baxter Equation KW - Lattice Effect Algebras CR - [1] Baxter, R.J., Exactly Solved Models in Statistical Mechanics, Academy Press: London, UK, 1982. CR - [2] Baxter, R.J., Partition function of the eight-vertex lattice model. Annals of Physics 1972, (70)1, 193–228. CR - [3] Borzooei, R.A., Dvurecenskij, A., and Sharafi, A.H. Material Implications in Lattice Effect Algebras, Information Sciences 433-434 2018 , 233-240. CR - [4] Botur, M., Chajda, I., Halas, R., K¨uhr, J., Paseka, J., “Algebraic Methods in Quantum Logic”, 1st ed. Palack´y University, Olomouc, 2014. CR - [5] Dalla Chiara, M. L, Giuntini, R., Greechie, R., “Reasoning in Quantum Theory: Sharp and Unsharp Quantum Logics” Springer, Netherlands, 2004. CR - [6] Drinfeld, V. G., On unsolved problems in quantum group theory. Quantum Groups, Lecture Notes Math. 1510, Springer-Verlag, Berlin, 1992, 1–8. CR - [7] Dvurecenskij, A. , Pulmannova, S., New Trends in Quantum Structures, Springer, Netherlands, 2000. CR - [8] Foulis, D.J., Bennett, M.K., Effect Algebras and Unsharp Quantum Logics, Found. Phys. 24 (1994), 1331–1352. CR - [9] Kassel, C., Quantum Groups, Graduate Text in Mathematics 155, Springer-Verlag, New York, 1995. CR - [10] Nichita, F.F., Special Issue “Hopf Algebras, Quantum Groups and Yang–Baxter Equations. Available online: http://www.mdpi.com/journal/axioms/special issues/hopf algebras 2014. CR - [11] Nichita, F.F., Introduction to the Yang-Baxter Equation with Open Problems Axioms 2012, 4, 423–435. CR - [12] Oner, T. Kalkan, T., Yang-Baxter Equations in MTL-algebras.. Bulletin of the International Mathematical Virtual Institute 2019, 9, 599–607. CR - [13] Oner, T. Katıcan, T., On solution to the Set-Theoretical Yang-Baxter Equation via BL-Algebras. Bulletin of the International Mathematical Virtual Institute 2019, 9, 207–217. CR - [14] Oner, T., Katıcan, T., On solutions to the Set-Theoretical Yang-Baxter Equation in Wasjberg-Algebras. Axioms 2018, 7, 6 . CR - [15] Perk, J.H.H., Au, Y.H., Yang-Baxter Equations. In Encyclopedia of Mathematical Physics; Franc¸oise, J.-P., Naber, G.L., Tsou S.T., Eds.; Elseiver: Oxford, UK 2006, 5, 465–473. CR - [16] Yang, C.N., Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 1967, 19, 1312–1315. UR - https://dergipark.org.tr/en/pub/konuralpjournalmath/issue//591417 L1 - https://dergipark.org.tr/en/download/article-file/1069494 ER -