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Year 2020, Volume: 8 Issue: 1, 106 - 113, 15.04.2020

Tahsin Öner Tuğçe Kalkan Alper Ülker

Abstract

References

  • [1] Baxter, R.J., Exactly Solved Models in Statistical Mechanics, Academy Press: London, UK, 1982.
  • [2] Baxter, R.J., Partition function of the eight-vertex lattice model. Annals of Physics 1972, (70)1, 193–228.
  • [3] Borzooei, R.A., Dvurecenskij, A., and Sharafi, A.H. Material Implications in Lattice Effect Algebras, Information Sciences 433-434 2018 , 233-240.
  • [4] Botur, M., Chajda, I., Halas, R., K¨uhr, J., Paseka, J., “Algebraic Methods in Quantum Logic”, 1st ed. Palack´y University, Olomouc, 2014.
  • [5] Dalla Chiara, M. L, Giuntini, R., Greechie, R., “Reasoning in Quantum Theory: Sharp and Unsharp Quantum Logics” Springer, Netherlands, 2004.
  • [6] Drinfeld, V. G., On unsolved problems in quantum group theory. Quantum Groups, Lecture Notes Math. 1510, Springer-Verlag, Berlin, 1992, 1–8.
  • [7] Dvurecenskij, A. , Pulmannova, S., New Trends in Quantum Structures, Springer, Netherlands, 2000.
  • [8] Foulis, D.J., Bennett, M.K., Effect Algebras and Unsharp Quantum Logics, Found. Phys. 24 (1994), 1331–1352.
  • [9] Kassel, C., Quantum Groups, Graduate Text in Mathematics 155, Springer-Verlag, New York, 1995.
  • [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.
  • [11] Nichita, F.F., Introduction to the Yang-Baxter Equation with Open Problems Axioms 2012, 4, 423–435.
  • [12] Oner, T. Kalkan, T., Yang-Baxter Equations in MTL-algebras.. Bulletin of the International Mathematical Virtual Institute 2019, 9, 599–607.
  • [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.
  • [14] Oner, T., Katıcan, T., On solutions to the Set-Theoretical Yang-Baxter Equation in Wasjberg-Algebras. Axioms 2018, 7, 6 .
  • [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.
  • [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.

Yang-Baxter Equation in Lattice Effect Algebras

Year 2020, Volume: 8 Issue: 1, 106 - 113, 15.04.2020

Tahsin Öner Tuğçe Kalkan Alper Ülker

Abstract

In this paper, we present lattice effect algebra by giving certain definitions and conceptions as to lattice effect algebra. We present new solutions to the set-theoratical Yang-Baxter equation by using lattice effect algebras.



Keywords

Yang–Baxter Equation Lattice Effect Algebras

References

  • [1] Baxter, R.J., Exactly Solved Models in Statistical Mechanics, Academy Press: London, UK, 1982.
  • [2] Baxter, R.J., Partition function of the eight-vertex lattice model. Annals of Physics 1972, (70)1, 193–228.
  • [3] Borzooei, R.A., Dvurecenskij, A., and Sharafi, A.H. Material Implications in Lattice Effect Algebras, Information Sciences 433-434 2018 , 233-240.
  • [4] Botur, M., Chajda, I., Halas, R., K¨uhr, J., Paseka, J., “Algebraic Methods in Quantum Logic”, 1st ed. Palack´y University, Olomouc, 2014.
  • [5] Dalla Chiara, M. L, Giuntini, R., Greechie, R., “Reasoning in Quantum Theory: Sharp and Unsharp Quantum Logics” Springer, Netherlands, 2004.
  • [6] Drinfeld, V. G., On unsolved problems in quantum group theory. Quantum Groups, Lecture Notes Math. 1510, Springer-Verlag, Berlin, 1992, 1–8.
  • [7] Dvurecenskij, A. , Pulmannova, S., New Trends in Quantum Structures, Springer, Netherlands, 2000.
  • [8] Foulis, D.J., Bennett, M.K., Effect Algebras and Unsharp Quantum Logics, Found. Phys. 24 (1994), 1331–1352.
  • [9] Kassel, C., Quantum Groups, Graduate Text in Mathematics 155, Springer-Verlag, New York, 1995.
  • [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.
  • [11] Nichita, F.F., Introduction to the Yang-Baxter Equation with Open Problems Axioms 2012, 4, 423–435.
  • [12] Oner, T. Kalkan, T., Yang-Baxter Equations in MTL-algebras.. Bulletin of the International Mathematical Virtual Institute 2019, 9, 599–607.
  • [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.
  • [14] Oner, T., Katıcan, T., On solutions to the Set-Theoretical Yang-Baxter Equation in Wasjberg-Algebras. Axioms 2018, 7, 6 .
  • [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.
  • [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.
There are 16 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Tahsin Öner

Tuğçe Kalkan This is me

Alper Ülker This is me

Publication Date April 15, 2020
Submission Date July 13, 2019
Acceptance Date March 28, 2020
Published in Issue Year 2020 Volume: 8 Issue: 1

Cite

APA Öner, T., Kalkan, T., & Ülker, A. (2020). Yang-Baxter Equation in Lattice Effect Algebras. Konuralp Journal of Mathematics, 8(1), 106-113.
AMA Öner T, Kalkan T, Ülker A. Yang-Baxter Equation in Lattice Effect Algebras. Konuralp J. Math. April 2020;8(1):106-113.
Chicago Öner, Tahsin, Tuğçe Kalkan, and Alper Ülker. “Yang-Baxter Equation in Lattice Effect Algebras”. Konuralp Journal of Mathematics 8, no. 1 (April 2020): 106-13.
EndNote Öner T, Kalkan T, Ülker A (April 1, 2020) Yang-Baxter Equation in Lattice Effect Algebras. Konuralp Journal of Mathematics 8 1 106–113.
IEEE T. Öner, T. Kalkan, and A. Ülker, “Yang-Baxter Equation in Lattice Effect Algebras”, Konuralp J. Math., vol. 8, no. 1, pp. 106–113, 2020.
ISNAD Öner, Tahsin et al. “Yang-Baxter Equation in Lattice Effect Algebras”. Konuralp Journal of Mathematics 8/1 (April 2020), 106-113.
JAMA Öner T, Kalkan T, Ülker A. Yang-Baxter Equation in Lattice Effect Algebras. Konuralp J. Math. 2020;8:106–113.
MLA Öner, Tahsin et al. “Yang-Baxter Equation in Lattice Effect Algebras”. Konuralp Journal of Mathematics, vol. 8, no. 1, 2020, pp. 106-13.
Vancouver Öner T, Kalkan T, Ülker A. Yang-Baxter Equation in Lattice Effect Algebras. Konuralp J. Math. 2020;8(1):106-13.
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