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1. Nikolaidou, Pipina. Το αλγεβρικό συνεχές και διακριτό στην κατασκευή ερευνητικών εργαλείων και στην επεξεργασία δεδομένων για τις επιστήμες αγωγής.

Degree: 2017, Democritus University of Thrace (DUTH); Δημοκρίτειο Πανεπιστήμιο Θράκης (ΔΠΘ)

Hyperstructures is a relatively new field in the area of Mathematics, given that only in 1934 Frederic Marty introduced this topic at the 8th Congress of Scandenavian Mathematicians, with his paper: “Sur une generalisation de la notion de groupe”, where the first definition of the hypergroup was given.Subsequently, F. Marty published two more papers [78], [79] and at the same time, many mathematicians such as H. Wall [154], J. Kuntzmann [71], M. Dresher and O.Ore [47], L. Griffiths [53], J. Eaton [50] και M. Krasner [68], started working on this subject, publishing the first relevant papers. Different types of hypergroups were studied, like the 'regular' ones by Wall & Kuntzmann and the 'reversible' ones by Dresher & Ore.The hyperstructure theory is based on the classical theory of algebraic structures and therefore, just like in the classical theory there are numerous applications both in groups ομάδες [49], [118], [48], [56], [96], [84], [112], [113], [114], [115], [54], [55] as well as in algebra [36], [67], [68] geometry and binary relations [110], [107], [109].W. Prenowitz [91] was the first to work on the application of geometry on hyperstructures, initially alone and later in cooperation with J. Jantosciak, with whom he defined the Join Spaces [92], [93]. In their book “Join Geometries”, despite the fact that the word hypergroup was not mentioned, the so called 'Join Spaces' appeared as a category of Hyperstructures, which was then studied by dozens of researchers. One of the main features of the books main characteristic is that the authors tried to describe geometrical problems in an algebraic way.M. Krasner's contribution to the timelessness of the hyperstructures was crucial, as he and his students preserved the hyperstructures by working on this field for several years, and the progress of the hyperstructures is largely attributed to them. In the book 'Il mondo Krasneriano', [94] P. Ribenboim referred to the mathematical work of M. Krasner and how he started dealing with the hyperstructures. Some of the most influential figures in the field of hyperstructures, such as Stratigopoulos, Mittas and Koguetsof, were M Krasner's students.Krasner introduced the structure hyperfield, a structure where the addition is an operation and the multiplication is a hyperoperation. This fact 'obliged' the structure to have some basic properties, which led to the canonical hyperstructure, studied mainly by Mitta and continued by Corsini. P. Corsini's work on the hypergroups was initiated by Mitta's paper, 'Canonical hypergroups'. Because of the fact that the canonical hypergroup is a very 'close' structure, it led to numerous theorems and conclusions.The study of hyperstructures expanded beyond the hypergroups. M. Krasner introduced the hyperfield [69] and 10 years later he defined the hyperring, where the addition is a hyperoperation and the multiplication is an operation. A new definition of the hyperring, given by R. Rota many years later [95], renamed it multiplicative hyperring, in which, contrary to Krasner's…

Subjects/Keywords: Υπερδομές; Ράβδος; Lie-Santilli admissible υπεράλγεβρες; Hv-δομές; Hyperstructures; Bar; Lie-Santilli admissible hyperalgebras; Hv-structures

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APA (6th Edition):

Nikolaidou, P. (2017). Το αλγεβρικό συνεχές και διακριτό στην κατασκευή ερευνητικών εργαλείων και στην επεξεργασία δεδομένων για τις επιστήμες αγωγής. (Thesis). Democritus University of Thrace (DUTH); Δημοκρίτειο Πανεπιστήμιο Θράκης (ΔΠΘ). Retrieved from http://hdl.handle.net/10442/hedi/40167

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Nikolaidou, Pipina. “Το αλγεβρικό συνεχές και διακριτό στην κατασκευή ερευνητικών εργαλείων και στην επεξεργασία δεδομένων για τις επιστήμες αγωγής.” 2017. Thesis, Democritus University of Thrace (DUTH); Δημοκρίτειο Πανεπιστήμιο Θράκης (ΔΠΘ). Accessed February 28, 2021. http://hdl.handle.net/10442/hedi/40167.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Nikolaidou, Pipina. “Το αλγεβρικό συνεχές και διακριτό στην κατασκευή ερευνητικών εργαλείων και στην επεξεργασία δεδομένων για τις επιστήμες αγωγής.” 2017. Web. 28 Feb 2021.

Vancouver:

Nikolaidou P. Το αλγεβρικό συνεχές και διακριτό στην κατασκευή ερευνητικών εργαλείων και στην επεξεργασία δεδομένων για τις επιστήμες αγωγής. [Internet] [Thesis]. Democritus University of Thrace (DUTH); Δημοκρίτειο Πανεπιστήμιο Θράκης (ΔΠΘ); 2017. [cited 2021 Feb 28]. Available from: http://hdl.handle.net/10442/hedi/40167.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Nikolaidou P. Το αλγεβρικό συνεχές και διακριτό στην κατασκευή ερευνητικών εργαλείων και στην επεξεργασία δεδομένων για τις επιστήμες αγωγής. [Thesis]. Democritus University of Thrace (DUTH); Δημοκρίτειο Πανεπιστήμιο Θράκης (ΔΠΘ); 2017. Available from: http://hdl.handle.net/10442/hedi/40167

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation


Universidade Estadual de Campinas

2. Biânchi, Angelo Calil, 1984-. Representações de hiperálgebras de laços e álgebras de multi-correntes: Representations of hyper loop algebras and multi curret algebras.

Degree: 2012, Universidade Estadual de Campinas

Abstract: This work is dedicated to the study of some aspects of the representation theory of certain algebras which can be regarded as generalizations of the concept of affine Kac- Moody algebras. The work is divided into two parts: the first is concerned with the finite-dimensional representations of twisted hyper loop algebras and the other focuses on certain homological properties of the category of representations of a multigraded Lie algebra which are useful to study a generalization of the concept of Kirillov-Reshetikhin modules Advisors/Committee Members: UNIVERSIDADE ESTADUAL DE CAMPINAS (CRUESP), Moura, Adriano Adrega de, 1975- (advisor), Chari, Vyjayanthi (coadvisor), Universidade Estadual de Campinas. Instituto de Matemática, Estatística e Ciência da Computação (institution), Programa de Pós-Graduação em Matemática (nameofprogram), Guerreiro, Marines (committee member), Kochloukov, Plamen Emilov (committee member), Bekkert, Viktor (committee member), Futorny, Vyacheslav (committee member).

Subjects/Keywords: Kac-Moody, Algebras de; Representações de álgebras; Fórmulas de caracteres; Álgebras graduadas; Kac-Moody algebras; Representations of algebras; Hyperalgebras; Character formulas; Graded algebras

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Biânchi, Angelo Calil, 1. (2012). Representações de hiperálgebras de laços e álgebras de multi-correntes: Representations of hyper loop algebras and multi curret algebras. (Thesis). Universidade Estadual de Campinas. Retrieved from http://repositorio.unicamp.br/jspui/handle/REPOSIP/307031

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Biânchi, Angelo Calil, 1984-. “Representações de hiperálgebras de laços e álgebras de multi-correntes: Representations of hyper loop algebras and multi curret algebras.” 2012. Thesis, Universidade Estadual de Campinas. Accessed February 28, 2021. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307031.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Biânchi, Angelo Calil, 1984-. “Representações de hiperálgebras de laços e álgebras de multi-correntes: Representations of hyper loop algebras and multi curret algebras.” 2012. Web. 28 Feb 2021.

Vancouver:

Biânchi, Angelo Calil 1. Representações de hiperálgebras de laços e álgebras de multi-correntes: Representations of hyper loop algebras and multi curret algebras. [Internet] [Thesis]. Universidade Estadual de Campinas; 2012. [cited 2021 Feb 28]. Available from: http://repositorio.unicamp.br/jspui/handle/REPOSIP/307031.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Biânchi, Angelo Calil 1. Representações de hiperálgebras de laços e álgebras de multi-correntes: Representations of hyper loop algebras and multi curret algebras. [Thesis]. Universidade Estadual de Campinas; 2012. Available from: http://repositorio.unicamp.br/jspui/handle/REPOSIP/307031

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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