Finite Dimensional Indecomposable Representations of the Poincare Algebra

1986 ◽  
pp. 185-195
Author(s):  
Bruno Gruber ◽  
Romuald Lenczewski
Keyword(s):  
Indecomposable Representations ◽  
Finite Dimensional ◽  
Poincaré Algebra

CONSTRUCTING FULL BLOCK TRIANGULAR REPRESENTATIONS OF ALGEBRAS

2007 ◽  
Vol 06 (02) ◽  
pp. 259-265
Author(s):  
DANIEL BIRMAJER
Keyword(s):  
Dimensional Representation ◽  
Finite Dimensional Representation ◽  
Direct Sum ◽  
Indecomposable Representations ◽  
Finite Dimensional ◽  
Triangular Representation ◽  
Representations Of Algebras ◽  
Finitely Presented ◽  
Complicated Task

Every finite dimensional representation of an algebra is equivalent to a finite direct sum of indecomposable representations. Hence, the classification of indecomposable representations of algebras is a relevant (and usually complicated) task. In this note we study the existence of full block triangular representations, an interesting example of indecomposable representations, from a computational perspective. We describe an algorithm for determining whether or not an associative finitely presented k-algebra R has a full block triangular representation over [Formula: see text].

scholarly journals On the representation theory of the infinite Temperley–Lieb algebra

2020 ◽  
pp. 2150205
Author(s):  
Stephen T. Moore
Keyword(s):  
Representation Theory ◽  
Spin Chain ◽  
Link State ◽  
Indecomposable Representations ◽  
Finite Dimensional ◽  
Weyl Duality

We begin the study of the representation theory of the infinite Temperley–Lieb algebra. We fully classify its finite-dimensional representations, then introduce infinite link state representations and classify when they are irreducible or indecomposable. We also define a construction of projective indecomposable representations for TL[Formula: see text] that generalizes to give extensions of TL[Formula: see text] representations. Finally, we define a generalization of the spin chain representation and conjecture a generalization of Schur–Weyl duality.

Some finite dimensional indecomposable representations of E(2)

1999 ◽  
Vol 40 (11) ◽  
pp. 6087-6109 ◽  
Author(s):  
Joe Repka ◽  
Hubert de Guise
Keyword(s):  
Indecomposable Representations ◽  
Finite Dimensional

CONSTRUCTION OF GENERAL COLORED R MATRICES FOR THE YANG-BAXTER EQUATION AND q-BOSON REALIZATION OF QUANTUM ALGEBRA slq(2) WHEN q IS A ROOT OF UNITY

1992 ◽  
Vol 07 (26) ◽  
pp. 6609-6622 ◽  
Author(s):  
MO-LIN GE ◽  
CHANG-PU SUN ◽  
KANG XUE
Keyword(s):  
Quantum Algebra ◽  
Baxter Equation ◽  
R Matrix ◽  
Root Of Unity ◽  
Indecomposable Representations ◽  
Finite Dimensional ◽  
Boson Realization ◽  
Independent Parameters

Through a general q-boson realization of quantum algebra sl q(2) and its universal R matrix an operator R matrix with many parameters is obtained in terms of q-boson operators. Building finite-dimensional representations of q-boson algebra, we construct various colored R matrices associated with nongeneric representations of sl q(2) with dimension-independent parameters. The “nonstandard” R matrices obtained by Lee-Couture and Murakami are their special examples. We also study the factorizable structure of some Rmatrices for the indecomposable representations used in its construction.

scholarly journals Representation theory of the algebra generated by a pair of complex structures

2020 ◽  
pp. 2150204
Author(s):  
Steven Gindi
Keyword(s):  
Representation Theory ◽  
Dihedral Group ◽  
Complex Structures ◽  
Real Numbers ◽  
The Real ◽  
Indecomposable Representations ◽  
Finite Dimensional

The objective of this paper is to determine the finite-dimensional, indecomposable representations of the algebra that is generated by two complex structures over the real numbers. Since the generators satisfy relations that are similar to those of the infinite dihedral group, we give the algebra the name [Formula: see text].

Finite Dimensional Representations of Ut(sl (2)) at Roots of Unity

1997 ◽  
Vol 49 (4) ◽  
pp. 772-787 ◽  
Author(s):  
Xiao Jie
Keyword(s):  
Roots Of Unity ◽  
Indecomposable Representations ◽  
Finite Dimensional

AbstractAll finite dimensional indecomposable representations of Ut(Sl (2)) at roots of 1 are determined.

Non-Linear Dynamics of Cardiovascular Variability Signals

1994 ◽  
Vol 33 (01) ◽  
pp. 81-84 ◽  
Author(s):  
S. Cerutti ◽  
S. Guzzetti ◽  
R. Parola ◽  
M.G. Signorini
Keyword(s):  
Dimensional Space ◽  
Severe Heart Failure ◽  
Parametric Models ◽  
Deterministic Systems ◽  
Finite Dimensional ◽  
Return Maps ◽  
Pathological Conditions ◽  
Non Linear ◽  
Space State

Abstract:Long-term regulation of beat-to-beat variability involves several different kinds of controls. A linear approach performed by parametric models enhances the short-term regulation of the autonomic nervous system. Some non-linear long-term regulation can be assessed by the chaotic deterministic approach applied to the beat-to-beat variability of the discrete RR-interval series, extracted from the ECG. For chaotic deterministic systems, trajectories of the state vector describe a strange attractor characterized by a fractal of dimension D. Signals are supposed to be generated by a deterministic and finite dimensional but non-linear dynamic system with trajectories in a multi-dimensional space-state. We estimated the fractal dimension through the Grassberger and Procaccia algorithm and Self-Similarity approaches of the 24-h heart-rate variability (HRV) signal in different physiological and pathological conditions such as severe heart failure, or after heart transplantation. State-space representations through Return Maps are also obtained. Differences between physiological and pathological cases have been assessed and generally a decrease in the system complexity is correlated to pathological conditions.

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