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In this short note we give a polynomial-time quantum reduction from the vectorization problem (DLP) to the parallelization problem (CDHP) for group actions. Combined with the trivial reduction from pa...
SeaSign: Compact isogeny signatures from class group actions
post-quantum crypto isogenies
2018/11/19
We give a new signature scheme for isogenies that combines the class group actions of CSIDH with the notion of Fiat-Shamir with aborts. Our techniques allow to have signatures of size less than one ki...
ERGODICITY OF MAPPING CLASS GROUP ACTIONS ON SU(2)-CHARACTER VAR IET IES
GROUP ACTIONS MAPPING CLASS
2015/9/29
Let be a compact orientable surface with genus g andnboundary components
∂1,..., ∂n. Let b = (b1,...,bn) ∈ [−2,2]
n. Then the mapping class group
Mod() acts on the relative SU(2)-...
Group actions on 4-manifolds: some recent results and open questions
Dynamic 4 - manifolds smooth symplectic classification group action
2014/12/24
A survey of finite group actions on symplectic 4-manifolds is given with a special emphasis on results and questions concerning smooth or symplectic classification of group actions, group actions and ...
A characterization of amenability of group actions on $C^\ast$-algebras
characterization amenability group actions $C^\ast$-algebras
2012/4/16
We show that coincidence of the full and reduced crossed product $C^\ast$-algebras of a group action on a unital commutative $C^\ast$-algebra implies amenability of the action whenever the group is ex...
Finite generators for countable group actions in the Borel and Baire category settings
Finite generators countable group actions Baire category settings Logic
2012/4/23
For a countable group G and a standard Borel G-space X, a countable Borel partition P of X is called a generator if {gA : g in G, A in P} generates the Borel sigma-algebra of X. For G=Z, the Kolmogoro...
A Lower Bound for the Number of Group Actions on a Compact Riemann Surface
Riemann surface automorphism signature mapping class group
2011/9/14
Abstract: We prove that the number of distinct group actions on compact Riemann surfaces of a fixed genus $\sigma \geq 2$ is at least quadratic in $\sigma$. We do this through the introduction of a co...
A refined form of the ‘Folk Theorem’ that a smooth action by a compact Lie group can be (canonically) resolved, by iterated blow up, to have unique isotropy type is proved in the context of manifolds ...
Nuclear and type I crossed products of C*-algebras by group and compact quantum group actions
Direct proofs Feigin-Fuchs character formula unitary representations Virasoro algebra
2011/3/1
Previously we gave a proof of the Feigin–Fuchs character formula for the irreducible unitary
discrete series of the Virasoro algebra with 0 < c < 1. The proof showed directly that the mutliplicity sp...
Smooth Lie group actions are parametrized diffeological subgroups
Smooth Lie group actions parametrized diffeological subgroups
2011/1/17
We show that every effective smooth action of a Lie group G on a manifold M is a diffeomorphism from G onto its image in Diff(M), where the image is equipped with the subset
diffeology of the functio...
We produce for each natural number n 3 two 1–parameter fam-ilies of Riemann surfaces admitting automorphism groups with two cyclic sub-groups H1 and H2 of orden 2n, that are conjugate in the group o...
Non-linear Group Actions with Polynomial Invariant Rings and a Structure Theorem for Modular Galois Extensions
Non-linear Group Polynomial Invariant Rings
2010/11/24
Let $G$ be a finite $p$-group and $k$ a field of characteristic $p>0$. We show that $G$ has a \emph{non-linear} faithful action on a polynomial ring $U$ of dimension $n=\mathrm{log}_p(|G|)$ such that...
Do absolutely irreducible group actions have odd dimensional fixed point spaces?
odd dimensional fixed point
2010/11/23
In his volume [5] on "Symmetry Breaking for Compact Lie Groups" Mike Field quotes a private communication by Jorge Ize claiming that any bifurcation problem with absolutely irreducible group action wo...
Holomorphic families of non-equivalent embeddings and of holomorphic group actions on affine space
Holomorphic families of non-equivalent embeddings holomorphic group affine space
2010/11/19
We construct holomorphic families of proper holomorphic embeddings of $\C^k$ into $\C^n$ ($0 so that for any two different parameters in the family no holomorphic automorphism of $\C^n$ can ...
Finite group actions, rational fixed points and weak Néron models
Finite group actions rational fixed points weak Néron models
2010/12/1
If G is a finite ℓ-group acting on an affine space An over a finite field K of cardinality prime to ℓ, Serre [29] shows that there exists a rational fixed point. We generalize this to the ...