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Separating invariants and local cohomology [PDF]
Advances in Mathematics, 2015 The study of separating invariants is a recent trend in invariant theory. For a finite group acting linearly on a vector space, a separating set is a set of invariants whose elements separate the orbits of G. In some ways, separating sets often exhibit better behavior than generating sets for the ring of invariants.
Emilie Dufresne, Jack Jeffries
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Journal of Symbolic Computation, 2009 The author defines a general notion of a separating subset. Explicitly, let \(X\) and \(K\) be sets (\(K\) will be a field or an integral domain in most situations), and let \(K^X\) be the set of all functions from \(X\) to \(K\). Let \(F\) be any subset of \(K^X\). A subset \(S\) of \(F\) is called an \(F\)-separating set if, for any \(x,y \in X\), if
Gregor Kemper
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Constructing modular separating invariants [PDF]
Journal of Algebra, 2009 Consider a finite dimensional representation \(V\) of a group \(G\) over a field \(F\). The induced action on the dual \(V^*\) extends to an action by algebra automorphisms on the symmetric algebra \(F[V]:=S(V^*)\). The elements of \(F[V]\) represent polynomial functions on \(V\). An invariant polynomial \(f\in F[V]^G\) is constant on \(G\)-orbits. For
Müfit Sezer
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Degree bounds for separating invariants [PDF]
Mathematical Research Letters, 2010 If V is a representation of a linear algebraic group G, a set S of G-invariant regular functions on V is called separating if the following holds: If two elements v,v' from V can be separated by an invariant function, then there is an f from S such that f(v) is different from f(v'). It is known that there always exist finite separating sets.
Martin Kohls
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Separating G2-invariants of several octonions [PDF]
Algebra and Number Theory, 2023 We describe separating G_2-invariants of several copies of the algebra of octonions over an algebraically closed field of characteristic two. We also obtain a minimal separating and a minimal generating set for G_2-invariants of several copies of the algebra of octonions in case of a field of odd characteristic.
Artem Lopatin
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Explicit separating invariants for cyclic P-groups [PDF]
Journal of Combinatorial Theory - Series A, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Müfit Sezer
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A Standardized Prism-Based TIRF Platform for Quantitative Single-Molecule Fluorescence Studies of Biomolecular Dynamics [PDF]
BiosensorsSingle-molecule Förster resonance energy transfer (smFRET) enables direct measurement of nanoscale conformational dynamics and heterogeneity in biomolecules, but quantitative interpretation of smFRET data critically depends on well-controlled excitation ...
Arijit Patra +4 more
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Separating invariants for 2 × 2 matrices [PDF]
Linear Algebra and Its Applications, 2018 A minimal separating set is found for the algebra of matrix invariants of several 2x2 matrices over an infinite field of arbitrary ...
Ivan Kaygorodov +2 more
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Separating invariants of finite groups [PDF]
Journal of Algebra, 2018 23 ...
Fabian Reimers
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Typical separating invariants [PDF]
Transformation Groups, 2007 It is shown that a trivial version of polarization is sufficient to produce separating systems of polynomial invariants: if two points in the direct sum of the $G$--modules $W$ and $m$ copies of $V$ can be separated by polynomial invariants, then they can be separated by invariants depending only on at most $2\dim(V)$ variables of type $V$; when $G$ is
M Domokos
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