کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4665638 1633824 2014 28 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Permanents, Doty coalgebras and dominant dimension of Schur algebras
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Permanents, Doty coalgebras and dominant dimension of Schur algebras
چکیده انگلیسی

A (hidden) multiplication on AZ(n,r)AZ(n,r), the ZZ-dual of the integral Schur algebra SZ(n,r)SZ(n,r) is explicitly constructed, possibly without a unit. The image of the multiplication map is shown to be spanned by bipermanents. Let k   be any field of characteristic p>0p>0. The image of the induced multiplication on Ak(n,r)=AZ(n,r)⊗ZkAk(n,r)=AZ(n,r)⊗Zk turns out to coincide with the Doty coalgebra Dn,r,pDn,r,p of truncated symmetric powers. Combined with a new straightening formula for bipermanents, it is proved that such a multiplication induces an isomorphism Ak(n,r)⊗Sk(n,r)Ak(n,r)≅Ak(n,r)Ak(n,r)⊗Sk(n,r)Ak(n,r)≅Ak(n,r) as Sk(n,r)Sk(n,r)-bimodules if and only if r≤n(p−1)r≤n(p−1), if and only if Dn,r,p=Ak(n,r)Dn,r,p=Ak(n,r). As a result, Sk(n,r)Sk(n,r) is a gendo-symmetric algebra, and its dominant dimension is at least two and admits a combinatorial characterization as long as r≤n(p−1)r≤n(p−1).

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 264, 20 October 2014, Pages 155–182
نویسندگان
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