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Dubois-Violette, Michel; Popov, Todor

doi:10.1023/a:1020770601601

Cited by 29 publications

(17 citation statements)

References 18 publications

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“…anti-commutative) algebras and related quantum spaces A n|0 q (resp. A 0|n q ) [19], • (Section 3.2) Drinfeld cotwists of a bialgebra in H N Alg, • (Section 3.5) the cubic Artin-Schelter regular algebras of type S 1 [1], and consequently the plactic and the parafermionic algebras with two generators (see [6] and references therein).…”

Section: Preliminariesmentioning

confidence: 99%

“…Since A 1 B 1 we can use this isomorphism, namely %, to deÿne # n : A ⊗n 1 → B ⊗n 1 for n ¡ N as # n = % ⊗n . Now, let us ÿx an integer n ¿ N ; (i) choose a basis of By last, let us mention that twisting process provides a convenient way for studying the relationship between quantum symmetries of these algebras [6,20].…”

Section: Theorem 14 Givenmentioning

confidence: 99%

“…Here we presented them using the notation of [6]. In particular, B = A 1; 1 is the parafermionic algebra, and P = A 0; 1 is the plactic algebra.…”

Section: Artin-schelter Algebras and Their Quantum Symmetriesmentioning

confidence: 99%

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Twisting of homogeneous algebras

Grillo

2004

Journal of Pure and Applied Algebra

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Twisting process for homogeneous algebras is deÿned. It consists of a particular kind of actual deformations controlled by a multiplicative cosimplicial quasicomplex C • related to each homogeneous algebra. The elements implementing twist transformations are a subclass of the counital 2-cocycles of C • . Such transformations are studied by means of their co-homological properties. It is shown they deÿne an equivalence relation between homogeneous algebras, in such a way that cubic Artin-Schelter regular algebras of type S1 (including parafermionic and plactic algebras with two generators) belong to the same class.

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Section: Preliminariesmentioning

confidence: 99%

Section: Theorem 14 Givenmentioning

confidence: 99%

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Twisting of homogeneous algebras

Grillo

2004

Journal of Pure and Applied Algebra

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“…Green [5](see also [3]). Here we will concentrate on the case when V is an ordinary (even) vector space V , when the algebra Ug is the parafermionic algebra.…”

Section: Introductionmentioning

confidence: 99%

Homotopy Commutative Algebra and 2-Nilpotent Lie Algebra

Dubois-Violette

Popov

2014

Springer Proceedings in Mathematics &Amp; Statistics

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“…that is, the factor of the tensor algebra T (V ) by the ideal I(V ) generated by the double supercommutators [8].…”

Section: Introductionmentioning

confidence: 99%

Parastatistics Algebra, Young Tableaux and the Super Plactic Monoid

Loday¹,

Popov

2008

Int. J. Geom. Methods Mod. Phys.

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Abstract. The parastatistics algebra is a superalgebra with (even) parafermi and (odd) parabose creation and annihilation operators. The states in the parastatistics Fock-like space are shown to be in one-to-one correspondence with the Super Semistandard Young Tableaux (SSYT) subject to further constraints. The deformation of the parastatistics algebra gives rise to a monoidal structure on the SSYT which is a super-counterpart of the plactic monoid.a Michel découvreur de senties inconnus où la beauté mathématique rejoint la simplicité des lois de la physique.

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Cited by 29 publications

References 18 publications

Twisting of homogeneous algebras

Twisting of homogeneous algebras

Homotopy Commutative Algebra and 2-Nilpotent Lie Algebra

Parastatistics Algebra, Young Tableaux and the Super Plactic Monoid

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