کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8905238 | 1633894 | 2018 | 44 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A propos de l'algèbre de Hopf des mots tassés WMat
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
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چکیده انگلیسی
In this article we study the packed words Hopf algebra WMat introduced by Duchamp, Hoang-Nghia et Tanasa. We start by explaining that WMat is not cofree, giving its antipode and describing its graded dual. We consider then a Hopf sub-algebra of permutations called SH. Its graded dual SHâ has a quadri-algebra structure, so it has a double dendriform algebra structure too. Thereafter, we introduce ISPW, a Hopf algebra of increasing strict packed words. It is graded, connected and cocommutative so is isomorphic to the enveloping algebra of its primitive elements. We describe some families of primitive elements. We prove that ISPW and non commutative symmetric functions are isomorphic. We define then an extended compositions Hopf algebra Ce. It is not cocommutative but its primitive elements and those from ISPW are linked. We give an interpretation of Ce in terms of a semi-direct coproduct Hopf algebra. By using this, we can define two actions groups. We finish by giving an explicit isomorphism between ISPWâ and QSym and another one between ISPW and NSym.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Bulletin des Sciences Mathématiques - Volume 145, June 2018, Pages 53-96
Journal: Bulletin des Sciences Mathématiques - Volume 145, June 2018, Pages 53-96
نویسندگان
Cécile Mammez,