Degree bounds for semi-invariant rings of quivers
نویسندگان
چکیده
منابع مشابه
A New Degree Bound for Invariant Rings
In this paper we give a new degree bound for polynomial invariant rings of finite groups and give some applications.
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Let G be a nite group acting as algebra automorphisms on A := FX 1 ; : : : ; Xn]. If F is a eld of characteristic zero, then, due to classical results of Emmy Noether one knows that the invariant ring A G can be generated in degrees less or equal to jGj. If F an arbitrary commutative ring (e.g. a nite eld), the situation is much less satisfying. In this paper we give an outline on known results...
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We study the left-right action of SL n × SL n on m-tuples of n × n matrices with entries in an infinite field K. We show that invariants of degree n 2 − n define the null cone. Consequently, invariants of degree ≤ n 6 generate the ring of invariants if char(K) = 0. We also prove that for m ≫ 0, invariants of degree at least n⌊ √ n + 1⌋ are required to define the null cone. We generalize our res...
متن کاملRank functors and representation rings of quivers
To my wife Kelly. ii ACKNOWLEDGEMENTS I would like to thank, first and foremost, my advisor Harm Derksen for guiding me along the path to becoming a mathematical researcher. The many hours we spent in discussion and his creative suggestions were absolutely essential for completion of this project. I would also like to thank John Stembridge for reading this dissertation and for some helpful disc...
متن کاملA note on the bounds of Laplacian-energy-like-invariant
The Laplacian-energy-like of a simple connected graph G is defined as LEL:=LEL(G)=∑_(i=1)^n√(μ_i ), Where μ_1 (G)≥μ_2 (G)≥⋯≥μ_n (G)=0 are the Laplacian eigenvalues of the graph G. Some upper and lower bounds for LEL are presented in this note. Moreover, throughout this work, some results related to lower bound of spectral radius of graph are obtained using the term of ΔG as the num...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2018
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2017.12.007