scholarly journals Representation theory of three-dimensional Sklyanin algebras

2012 ◽  
Vol 860 (1) ◽  
pp. 167-185 ◽  
Author(s):  
Chelsea Walton
Keyword(s):  
Representation Theory ◽  
Three Dimensional ◽  
Sklyanin Algebras

scholarly journals Quotients of degenerate Sklyanin algebras

2017 ◽  
Vol 16 (05) ◽  
pp. 1750085 ◽  
Author(s):  
Kevin De Laet
Keyword(s):  
Heisenberg Group ◽  
Hilbert Series ◽  
Three Dimensional ◽  
Central Element ◽  
Sklyanin Algebras ◽  
Sklyanin Algebra

In this paper, it is shown how the Heisenberg group of order 27 can be used to construct quotients of degenerate Sklyanin algebras. These quotients have properties similar to the classical Sklyanin case in the sense that they have the same Hilbert series, the same character series and a central element of degree 3. Regarding the central element of a three-dimensional Sklyanin algebra, a better way to view this using Heisenberg-invariants is shown.

scholarly journals Ideal classes of three-dimensional Sklyanin algebras

2004 ◽  
Vol 276 (2) ◽  
pp. 515-551 ◽  
Author(s):  
Koen de Naeghel ◽  
Michel van den Bergh
Keyword(s):  
Three Dimensional ◽  
Sklyanin Algebras

scholarly journals Three dimensional Sklyanin algebras and Gröbner bases

2017 ◽  
Vol 470 ◽  
pp. 379-419 ◽  
Author(s):  
Natalia Iyudu ◽  
Stanislav Shkarin
Keyword(s):  
Gröbner Bases ◽  
Three Dimensional ◽  
Grobner Bases ◽  
Sklyanin Algebras

scholarly journals Three-dimensional equations of generalized dynamics of 18-fold symmetry soft-matter quasicrystals

2020 ◽  
Vol 34 (11) ◽  
pp. 2050109
Author(s):  
Zhi-Yi Tang ◽  
Tian-You Fan
Keyword(s):  
Equation Of State ◽  
Representation Theory ◽  
Soft Matter ◽  
Group Representation ◽  
Three Dimensional ◽  
Governing Equations ◽  
Elementary Excitations ◽  
Group Representation Theory ◽  
Complete Form

This paper presents a three-dimensional form of governing equations of generalized dynamics of 18-fold symmetry soft-matter quasicrystals. According to the dynamics basis, there are first and second phason elementary excitations apart from phonons and fluid phonon. In the derivation, the group representation theory is a key point. The complete form of the theory includes an equation of state. The governing equations present some important meaning in the study on thermodynamics of the matter, which is also introduced.

scholarly journals Poisson geometry of PI three‐dimensional Sklyanin algebras

2018 ◽  
Vol 118 (6) ◽  
pp. 1471-1500
Author(s):  
Chelsea Walton ◽  
Xingting Wang ◽  
Milen Yakimov
Keyword(s):  
Three Dimensional ◽  
Poisson Geometry ◽  
Sklyanin Algebras

scholarly journals THE ALEXANDER AND JONES POLYNOMIALS THROUGH REPRESENTATIONS OF ROOK ALGEBRAS

2012 ◽  
Vol 21 (12) ◽  
pp. 1250114 ◽  
Author(s):  
STEPHEN BIGELOW ◽  
ERIC RAMOS ◽  
REN YI
Keyword(s):  
Representation Theory ◽  
Braid Group ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Knot Invariants ◽  
Alexander Polynomials ◽  
Algebraic Setting ◽  
Jones Polynomials ◽  
Group B ◽  
Three Dimensional Space

In the 1920's Artin defined the braid group, Bn, in an attempt to understand knots in a more algebraic setting. A braid is a certain arrangement of strings in three-dimensional space. It is a celebrated theorem of Alexander that every knot is obtainable from a braid by identifying the endpoints of each string. Because of this correspondence, the Jones and Alexander polynomials, two of the most important knot invariants, can be described completely using the braid group. There has been a recent growth of interest in other diagrammatic algebras, whose elements have a similar topological flavor to the braid group. These have wide ranging applications in areas including representation theory and quantum computation. We consider representations of the braid group when passed through another diagrammatic algebra, the planar rook algebra. By studying traces of these matrices, we recover both the Jones and Alexander polynomials.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

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