Jacobi polynomials and generalized Clifford algebra-valued Appell sequences

2013 ◽  
Vol 37 (10) ◽  
pp. 1527-1537 ◽  
Author(s):  
Isabel Cação ◽  
David Eelbode
Keyword(s):  
Clifford Algebra ◽  
Jacobi Polynomials ◽  
Appell Sequences ◽  
Generalized Clifford Algebra

scholarly journals The generalized Clifford algebra and the unitary group

1969 ◽  
Vol 27 (1) ◽  
pp. 164-170 ◽  
Author(s):  
Alladi Ramakrishnan ◽  
P.S Chandrasekaran ◽  
N.R Ranganathan ◽  
T.S Santhanam ◽  
R Vasudevan
Keyword(s):  
Clifford Algebra ◽  
Unitary Group ◽  
Generalized Clifford Algebra

scholarly journals Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space

2004 ◽  
Vol 2004 (52) ◽  
pp. 2761-2772 ◽  
Author(s):  
Fred Brackx ◽  
Nele De Schepper ◽  
Frank Sommen
Keyword(s):  
Euclidean Space ◽  
Orthogonal Polynomials ◽  
Clifford Algebra ◽  
Unit Ball ◽  
Real Axis ◽  
Jacobi Polynomials ◽  
Orthogonality Relation ◽  
Weight Functions ◽  
Open Unit ◽  
Open Unit Ball

A new method for constructing Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space is presented. In earlier research, we only dealt with scalar-valued weight functions. Now the class of weight functions involved is enlarged to encompass Clifford algebra-valued functions. The method consists in transforming the orthogonality relation on the open unit ball into an orthogonality relation on the real axis by means of the so-called Clifford-Heaviside functions. Consequently, appropriate orthogonal polynomials on the real axis give rise to Clifford algebra-valued orthogonal polynomials in the unit ball. Three specific examples of such orthogonal polynomials in the unit ball are discussed, namely, the generalized Clifford-Jacobi polynomials, the generalized Clifford-Gegenbauer polynomials, and the shifted Clifford-Jacobi polynomials.

scholarly journals (q,σ,τ)-Differential Graded Algebras

Universe ◽  
2018 ◽  
Vol 4 (12) ◽  
pp. 138 ◽  
Author(s):  
Viktor Abramov ◽  
Olga Liivapuu ◽  
Abdenacer Makhlouf
Keyword(s):  
Clifford Algebra ◽  
Quantum Plane ◽  
Graded Algebra ◽  
Graded Algebras ◽  
Differential Graded Algebra ◽  
Differential Graded Algebras ◽  
Generalized Clifford Algebra

We propose the notion of ( q , σ , τ ) -differential graded algebra, which generalizes the notions of ( σ , τ ) -differential graded algebra and q-differential graded algebra. We construct two examples of ( q , σ , τ ) -differential graded algebra, where the first one is constructed by means of the generalized Clifford algebra with two generators (reduced quantum plane), where we use a ( σ , τ ) -twisted graded q-commutator. In order to construct the second example, we introduce the notion of ( σ , τ ) -pre-cosimplicial algebra.

scholarly journals Idempotent matrices from a generalized Clifford algebra

1969 ◽  
Vol 27 (3) ◽  
pp. 563-564 ◽  
Author(s):  
Alladi Ramakrishnan ◽  
P.S. Chandrasekaran ◽  
N.R. Ranganathan ◽  
T.S. Santhanam ◽  
R. Vasudevan
Keyword(s):  
Clifford Algebra ◽  
Generalized Clifford Algebra

scholarly journals Helicity matrices for generalized Clifford algebra

1969 ◽  
Vol 26 (2) ◽  
pp. 275-278 ◽  
Author(s):  
Alladi Ramakrishnan ◽  
T.S Santhanam ◽  
P.S Chandrasekaran ◽  
A Sundaram
Keyword(s):  
Clifford Algebra ◽  
Generalized Clifford Algebra
Sign in / Sign up

Export Citation Format

Share Document