scholarly journals Supersymmetry algebra cohomology. IV. Primitive elements in all dimensions from D = 4 to D = 11

2013 ◽  
Vol 54 (5) ◽  
pp. 052302 ◽  
Author(s):  
Friedemann Brandt
Keyword(s):  
Primitive Elements ◽  
Supersymmetry Algebra

scholarly journals A FOUR-DIMENSIONAL SUPERSTRING FROM THE BOSONIC STRING WITH SOME APPLICATIONS

2005 ◽  
Vol 20 (01) ◽  
pp. 99-128 ◽  
Author(s):  
B. B. DEO ◽  
L. MAHARANA
Keyword(s):  
Standard Model ◽  
Central Charge ◽  
Virasoro Algebra ◽  
Low Energy ◽  
Majorana Fermions ◽  
Modular Invariance ◽  
Model Group ◽  
Supersymmetry Algebra ◽  
Four Dimensions ◽  
Bosonic Representation

A string in four dimensions is constructed by supplementing it with 44 Majorana fermions. The later are represented by 11 vectors in the bosonic representation SO (D-1,1). The central charge is 26. The fermions are grouped in such a way that the resulting action is worldsheet supersymmetric. The energy–momentum and current generators satisfy the super-Virasoro algebra. GSO projections are necessary for proving modular invariance. Space–time supersymmetry algebra is deduced and is substantiated for specific modes of zero mass. The symmetry group of the model can descend to the low energy standard model group SU (3)× SU L(2)× U Y(1) through the Pati–Salam group.

scholarly journals Linear combinations of primitive elements of a finite field

2018 ◽  
Vol 51 ◽  
pp. 388-406 ◽  
Author(s):  
Stephen D. Cohen ◽  
Tomás Oliveira e Silva ◽  
Nicole Sutherland ◽  
Tim Trudgian
Keyword(s):  
Finite Field ◽  
Primitive Elements ◽  
Linear Combinations

scholarly journals Comultiplication Rules for the Double Schur Functions and Cauchy Identities

10.37236/102 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
A. I. Molev
Keyword(s):  
Symmetric Functions ◽  
Schur Functions ◽  
Primitive Elements ◽  
Expansion Formula ◽  
New Family ◽  
Dual Object ◽  
Multiplication Rule ◽  
Distinguished Basis ◽  
Natural Way

The double Schur functions form a distinguished basis of the ring $\Lambda(x\!\parallel\!a)$ which is a multiparameter generalization of the ring of symmetric functions $\Lambda(x)$. The canonical comultiplication on $\Lambda(x)$ is extended to $\Lambda(x\!\parallel\!a)$ in a natural way so that the double power sums symmetric functions are primitive elements. We calculate the dual Littlewood–Richardson coefficients in two different ways thus providing comultiplication rules for the double Schur functions. We also prove multiparameter analogues of the Cauchy identity. A new family of Schur type functions plays the role of a dual object in the identities. We describe some properties of these dual Schur functions including a combinatorial presentation and an expansion formula in terms of the ordinary Schur functions. The dual Littlewood–Richardson coefficients provide a multiplication rule for the dual Schur functions.

scholarly journals Perspectives pour la linguistique : de la linguistique descriptive à la linguistique explicative

2021 ◽  
Vol 33 ◽  
pp. 1-29
Author(s):  
Wiesław Banyś
Keyword(s):  
General Theory ◽  
Point Of View ◽  
Primitive Elements ◽  
Aim Of Science ◽  
The Difference ◽  
Main Components ◽  
General Linguistic ◽  
Object Of Study ◽  
Comprehensive Study

The text deals with one of the challenges of linguistics, which is to effectively combine description and explanation in linguistics.It is necessary that linguistic theories are not only capable of adequately describing their object of study within their framework, but they must also have a suitable explanatory power.Linguistics centred around the explanation of the why of the system is called here ‘explanatory’ or ‘non-autonomous’, in contrast to ‘descriptive’ or ‘autonomous’ linguistics, which is focused on the description of the system, the distinction being based on the difference in the objects of study, the goals and the descriptive and explanatory possibilities of the theories.From the point of view presented here, a comprehensive study of language has three main components: a general theory of what language is, a resulting theory and description, which is a function of this theory, of how language is organised, functions and has evolved in the human brain, and an explanation of the properties of language found.The explanatory value of a general linguistic theory is a function of various elements, among others, the quantity of the primitive elements of the theory adopted and the effectiveness of Ockham’s razor principle of simplicity. It is also a function of the quality of those elements which can be drawn not only from within the system, but also from outside the system becoming in this situation logically prior to the object under study.In science, in linguistics, one naturally needs two types of approach, two types of linguistics, descriptive/autonomous and explanatory/non-autonomous, one must first describe reality in order to explain it. But it is also certain that since the aim of science is to explain in order to reach that higher level of scientificity above pure description, it is necessary that this aim be realized in different linguistic theories within different research programs, uniting descriptivist and explanatory approaches.

scholarly journals COUNTING PRIMITIVE ELEMENTS IN FREE GROUPS

2001 ◽  
Vol 10 ◽  
pp. 50-53
Author(s):  
J. Burillo ◽  
E. Ventura
Keyword(s):  
Free Groups ◽  
Primitive Elements

Existence of pair of primitive elements over finite fields of characteristic 2

2018 ◽  
Vol 193 ◽  
pp. 386-394 ◽  
Author(s):  
Rajendra K. Sharma ◽  
Ambrish Awasthi ◽  
Anju Gupta
Keyword(s):  
Finite Fields ◽  
Primitive Elements ◽  
Characteristic 2
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