On an Analog of Lagrange's Theorem for Commutative HOPF Algebras

1980 ◽  
Vol 79 (2) ◽  
pp. 164 ◽  
Author(s):  
David E. Radford
Keyword(s):  
Hopf Algebras ◽  
Lagrange's Theorem

scholarly journals Lagrange's Theorem for Hopf Monoids in Species

2013 ◽  
Vol 65 (2) ◽  
pp. 241-265 ◽  
Author(s):  
Marcelo Aguiar ◽  
Aaron Lauve
Keyword(s):  
Hopf Algebras ◽  
Necessary Conditions ◽  
Necessary Condition ◽  
Polynomial Inequalities ◽  
Generating Series ◽  
Pointed Hopf Algebras ◽  
Nonnegative Coefficients ◽  
Binomial Transform ◽  
Hopf Monoid ◽  
Lagrange's Theorem

AbstractFollowing Radford's proof of Lagrange's theorem for pointed Hopf algebras, we prove Lagrange‘s theorem for Hopf monoids in the category of connected species. As a corollary, we obtain necessary conditions for a given subspecies k of a Hopf monoid h to be a Hopf submonoid: the quotient of any one of the generating series of h by the corresponding generating series of k must have nonnegative coefficients. Other corollaries include a necessary condition for a sequence of nonnegative integers to be the dimension sequence of a Hopfmonoid in the formof certain polynomial inequalities and of a set-theoretic Hopf monoid in the form of certain linear inequalities. The latter express that the binomial transform of the sequence must be nonnegative.

Speed Enhancement Technique for Pulsed Laser Rangefinders Based on Lagrange's Theorem Using an Undersampling Method

2011 ◽  
Vol E94-A (8) ◽  
pp. 1738-1746
Author(s):  
Masahiro OHISHI ◽  
Fumio OHTOMO ◽  
Masaaki YABE ◽  
Mitsuru KANOKOGI ◽  
Takaaki SAITO ◽  
...  
Keyword(s):  
Pulsed Laser ◽  
Enhancement Technique ◽  
Lagrange's Theorem

Left counital Hopf algebras on bi-decorated planar rooted forests and Rota-Baxter systems

2020 ◽  
Vol 27 (2) ◽  
pp. 219-243 ◽  
Author(s):  
Xiao-Song Peng ◽  
Yi Zhang ◽  
Xing Gao ◽  
Yan-Feng Luo
Keyword(s):  
Hopf Algebras

scholarly journals Monadic cointegrals and applications to quasi-Hopf algebras

2021 ◽  
Vol 225 (10) ◽  
pp. 106678
Author(s):  
Johannes Berger ◽  
Azat M. Gainutdinov ◽  
Ingo Runkel
Keyword(s):  
Hopf Algebras

Quotients of hopf algebras

1978 ◽  
Vol 6 (17) ◽  
pp. 1789-1800 ◽  
Author(s):  
Warren D. Nichols
Keyword(s):  
Hopf Algebras

scholarly journals Bialgebra cohomology, pointed Hopf algebras, and deformations

2009 ◽  
Vol 213 (7) ◽  
pp. 1399-1417 ◽  
Author(s):  
Mitja Mastnak ◽  
Sarah Witherspoon
Keyword(s):  
Hopf Algebras ◽  
Pointed Hopf Algebras

scholarly journals Palatial Twistors from Quantum Inhomogeneous Conformal Symmetries and Twistorial DSR Algebras

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1309
Author(s):  
Jerzy Lukierski
Keyword(s):  
Phase Space ◽  
Hopf Algebras ◽  
Deformation Parameter ◽  
Heisenberg Algebra ◽  
Planck Length ◽  
Covariant Quantum ◽  
Drinfeld Twist ◽  
Quantum Deformations ◽  
Heisenberg Double ◽  
Conformal Symmetries

We construct recently introduced palatial NC twistors by considering the pair of conjugated (Born-dual) twist-deformed D=4 quantum inhomogeneous conformal Hopf algebras Uθ(su(2,2)⋉T4) and Uθ¯(su(2,2)⋉T¯4), where T4 describes complex twistor coordinates and T¯4 the conjugated dual twistor momenta. The palatial twistors are suitably chosen as the quantum-covariant modules (NC representations) of the introduced Born-dual Hopf algebras. Subsequently, we introduce the quantum deformations of D=4 Heisenberg-conformal algebra (HCA) su(2,2)⋉Hℏ4,4 (Hℏ4,4=T¯4⋉ℏT4 is the Heisenberg algebra of twistorial oscillators) providing in twistorial framework the basic covariant quantum elementary system. The class of algebras describing deformation of HCA with dimensionfull deformation parameter, linked with Planck length λp, is called the twistorial DSR (TDSR) algebra, following the terminology of DSR algebra in space-time framework. We describe the examples of TDSR algebra linked with Palatial twistors which are introduced by the Drinfeld twist and the quantization map in Hℏ4,4. We also introduce generalized quantum twistorial phase space by considering the Heisenberg double of Hopf algebra Uθ(su(2,2)⋉T4).

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