American Journal of Modern Physics

| Peer-Reviewed |

Hyper-Representations by Non Square Matrices Helix-Hopes

Received: 02 June 2015    Accepted: 02 June 2015    Published: 11 August 2015
Views:       Downloads:

Share This Article

Abstract

Hyperstructure theory can overcome restrictions which ordinary algebraic structures have. A hyperproduct on non-square ordinary matrices can be defined by using the so called helix-hyperoperations. We define and study the helix-hyperstructures on the representations and we extend our study up to Lie-Santilli theory by using ordinary fields. Therefore the related theory can be faced by defining the hyperproduct on the extended set of non square matrices. The obtained hyperstructure is an Hv-algebra or an Hv-Lie-alebra

DOI 10.11648/j.ajmp.s.2015040501.17
Published in American Journal of Modern Physics (Volume 4, Issue 5-1, October 2015)

This article belongs to the Special Issue Issue I: Foundations of Hadronic Mathematics

Page(s) 52-58
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Hyperstructures, Hv-Structures, H/V-Structures, Hope, Helix-Hope

References
[1] R. Bayon, N. Lygeros, Advanced results in enumeration of hyperstructures, J. Algebra, 320, 2008, 821-835.
[2] P. Corsini, V. Leoreanu, Applications of Hypergroup Theory, Kluwer Academic Publ., 2003.
[3] P. Corsini, T. Vougiouklis, From groupoids to groups through hypergroups, Rendiconti Mat. VII, 9, 1989, 173-181.
[4] B. Davvaz, On Hv-subgroups and anti fuzzy Hv-subgroups, Korean J. Comp. Appl. Math. V.5, N.1, 1998, 181-190.
[5] B. Davvaz, Fuzzy Hv-submodules, Fuzzy sets and Systems, 117, 2001, 477-484.
[6] B. Davvaz, A brief survey of the theory of Hv-structures, 8th AHA, Greece, Spanidis, 2003, 39-70.
[7] B. Davvaz, W. Dudek, T. Vougiouklis, A generalization of n-ary algebraic systems, Communications in Algebra, 37, 2009, 1248-1263.
[8] B. Davvaz, V. Leoreanu-Fotea, Hyperring Theory and Applications, Int. Academic Press, USA, 2007.
[9] B. Davvaz, R.M. Santilli, T. Vougiouklis, Multi-valued Hyper- mathematics for characterization of matter and antimatter systems, J. Computational Methods Sciences Eng. 13, 2013, 37–50.
[10] B. Davvaz, R.M. Santilli, T. Vougiouklis, Mathematical prediction of Ying’s twin universes, American J. Modern Physics, 4(3), 2015, 5-9.
[11] B. Davvaz, S. Vougioukli, T. Vougiouklis, On the multiplicative Hv-rings derived from helix hyperoperations, Util. Math., 84, 2011, 53-63.
[12] B. Davvaz, T. Vougiouklis, N-ary hypergroups, Iranian J. of Science & Technology, Transaction A, V.30, N.A2, 2006, 165-174.
[13] N. Lygeros, T. Vougiouklis, The LV-hyperstructures, Ratio Math., 25, 2013, 59–66.
[14] R.M. Santilli, Hadronic Mathematics, Mechanics and Chemistry, Vol. I, II, III, IV and V, Int. Academic Press, USA, 2008.
[15] R.M. Santilli, T. Vougiouklis, Isotopies, Genotopies, Hyperstructures and their Appl., Proc. New Frontiers in Hyperstructures and Related Algebras, Hadronic, 1996, 1-48.
[16] S. Vougiouklis, Hv-vector spaces from helix hyperoperations, Int. J. Math. Anal. (New Series), 1(2), 2009, 109-120.
[17] T. Vougiouklis, Cyclicity in a special class of hypergroups, Acta Un. Car. – Math. Et Ph., V.22, N1, 1981, 3-6.
[18] T. Vougiouklis, Representations of hypergroups, Hypergroup algebra, Proc. Convegno: ipergrouppi, altre strutture multivoche appl. Udine, 1985, 59-73.
[19] T. Vougiouklis, On affine Kac-Moody Lie algebras, Commentationes Math. Un. Car., V.26, 2, 1985, 387-395
[20] T. Vougiouklis, Representations of hypergroups by hyper- matrices, Rivista Mat. Pura Appl., N 2, 1987, 7-19.
[21] T. Vougiouklis, Generalization of P-hypergroups, Rend. Circ. Mat. Palermo, S.II, 36, 1987, 114-121.
[22] T. Vougiouklis, Groups in hypergroups, Annals of Discrete Math. 37, 1988, 459-468
[23] T. Vougiouklis, The fundamental relation in hyperrings. The general hyperfield, Proc. 4th AHA, World Scientific, 1991, 203-211.
[24] T. Vougiouklis, Representations of hypergroups by generalized permutations, Algebra Universalis, 29, 1992, 172-183.
[25] T. Vougiouklis, Representations of Hv-structures, Proc. Int. Conf. Group Theory 1992, Timisoara, 1993, 159-184.
[26] T. Vougiouklis, Hyperstructures and their Representations, Monographs in Math., Hadronic Press, 1994.
[27] T. Vougiouklis, Some remarks on hyperstructures, Contemp. Math., Amer. Math. Society, 184, 1995, 427-431.
[28] T. Vougiouklis, Enlarging Hv-structures, Algebras and Comb., ICAC’97, Hong Kong, Springer-Verlag, 1999, 455-463.
[29] T. Vougiouklis, On Hv-rings and Hv-representations, Discrete Math., Elsevier, 208/209, 1999, 615-620.
[30] T. Vougiouklis, Finite Hv-structures and their representations, Rend. Seminario Mat. Messina S.II, V.9, 2003, 245-265.
[31] T. Vougiouklis, The h/v-structures, J. Discrete Math. Sciences and Cryptography, V.6, 2003, N.2-3, 235-243.
[32] T. Vougiouklis, -operations and Hv-fields, Acta Math. Sinica, (Engl. Ser.), V.24, N.7, 2008, 1067-1078.
[33] T. Vougiouklis, The e-hyperstructures, J. Mahani Math. Research Center, V.1, N.1, 2012, 13-28.
[34] T. Vougiouklis, The Lie-hyperalebras and their fundamental relations, Southeast Asian Bull. Math., V.37(4), 2013, 601-614.
[35] T. Vougiouklis, Lie-admissible hyperalgebras, Italian J. Pure Applied Math., N.31, 2013,
[36] T. Vougiouklis, From Hv-rings to Hv-fields, Int. J. Algebraic Hyperstructures Appl. Vol.1, No.1, 2014, 1-13.
[37] T. Vougiouklis, Hypermatrix representations of finite Hv-groups, European J. Combinatorics, V.44 B, 2015, 307-315.
[38] T. Vougiouklis, Quiver of hyperstructures for Ying’s twin universes, American J. Modern Physics, 4(1-1), 2015, 30-33.
[39] T. Vougiouklis, S. Vougiouklis, The helix hyperoperations, Italian J. Pure Appl. Math., 18, 2005, 197-206.
[40] T. Vougiouklis, P. Kambaki-Vougioukli, On the use of the bar, China-USA Business Review, V.10, N.6, 2011, 484-489.
Author Information
  • Democritus University of Thrace, School of Education, Athens, Greece

  • Democritus University of Thrace, School of Education, Athens, Greece

Cite This Article
  • APA Style

    T. Vougiouklis, S. Vougiouklis. (2015). Hyper-Representations by Non Square Matrices Helix-Hopes. American Journal of Modern Physics, 4(5-1), 52-58. https://doi.org/10.11648/j.ajmp.s.2015040501.17

    Copy | Download

    ACS Style

    T. Vougiouklis; S. Vougiouklis. Hyper-Representations by Non Square Matrices Helix-Hopes. Am. J. Mod. Phys. 2015, 4(5-1), 52-58. doi: 10.11648/j.ajmp.s.2015040501.17

    Copy | Download

    AMA Style

    T. Vougiouklis, S. Vougiouklis. Hyper-Representations by Non Square Matrices Helix-Hopes. Am J Mod Phys. 2015;4(5-1):52-58. doi: 10.11648/j.ajmp.s.2015040501.17

    Copy | Download

  • @article{10.11648/j.ajmp.s.2015040501.17,
      author = {T. Vougiouklis and S. Vougiouklis},
      title = {Hyper-Representations by Non Square Matrices Helix-Hopes},
      journal = {American Journal of Modern Physics},
      volume = {4},
      number = {5-1},
      pages = {52-58},
      doi = {10.11648/j.ajmp.s.2015040501.17},
      url = {https://doi.org/10.11648/j.ajmp.s.2015040501.17},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajmp.s.2015040501.17},
      abstract = {Hyperstructure theory can overcome restrictions which ordinary algebraic structures have. A hyperproduct on non-square ordinary matrices can be defined by using the so called helix-hyperoperations. We define and study the helix-hyperstructures on the representations and we extend our study up to Lie-Santilli theory by using ordinary fields. Therefore the related theory can be faced by defining the hyperproduct on the extended set of non square matrices. The obtained hyperstructure is an Hv-algebra or an Hv-Lie-alebra},
     year = {2015}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - Hyper-Representations by Non Square Matrices Helix-Hopes
    AU  - T. Vougiouklis
    AU  - S. Vougiouklis
    Y1  - 2015/08/11
    PY  - 2015
    N1  - https://doi.org/10.11648/j.ajmp.s.2015040501.17
    DO  - 10.11648/j.ajmp.s.2015040501.17
    T2  - American Journal of Modern Physics
    JF  - American Journal of Modern Physics
    JO  - American Journal of Modern Physics
    SP  - 52
    EP  - 58
    PB  - Science Publishing Group
    SN  - 2326-8891
    UR  - https://doi.org/10.11648/j.ajmp.s.2015040501.17
    AB  - Hyperstructure theory can overcome restrictions which ordinary algebraic structures have. A hyperproduct on non-square ordinary matrices can be defined by using the so called helix-hyperoperations. We define and study the helix-hyperstructures on the representations and we extend our study up to Lie-Santilli theory by using ordinary fields. Therefore the related theory can be faced by defining the hyperproduct on the extended set of non square matrices. The obtained hyperstructure is an Hv-algebra or an Hv-Lie-alebra
    VL  - 4
    IS  - 5-1
    ER  - 

    Copy | Download

  • Sections