34 citations · 88 across the 20 of their papers we have counts for
25 papers
Additive diameters and covering complexity of irreducible representations
Urban Jezernik, Špela Špenko
Let a group act linearly on a finite-dimensional complex vector space . The group-additive diameter of a subspace is the least number of translates of whose s…
Additive diameters of group representations
Urban Jezernik, Špela Špenko
We explore the concept of additive diameters in the context of group representations, unifying various noncommutative Waring-type problems. Given a finite-dimensional representatio…
Perverse schobers and GKZ systems
Špela Špenko, Michel Van den Bergh
Perverse schobers are categorifications of perverse sheaves. In prior work we constructed a perverse schober on a partial compactification of the stringy Kähler moduli space (SKMS)…
Comparing the Kirwan and noncommutative resolutions of quotient varieties
Špela Špenko, Michel Van den Bergh
Let a reductive group act on a smooth variety such that a good quotient exists. We show that the derived category of a noncommutative crepant resolution (NCCR)…
A class of perverse schobers in Geometric Invariant Theory
Špela Špenko, Michel Van den Bergh
Perverse schobers are categorifications of perverse sheaves. We construct a perverse schober on a partial compactification of the stringy Kähler moduli space (SKMS) associated by H…
On the noncommutative Bondal-Orlov conjecture for some toric varieties
Špela Špenko, Michel Van den Bergh, with an appendix by Jason P. Bell
We show that all toric noncommutative crepant resolutions (NCCRs) of affine GIT quotients of "weakly symmetric" unimodular torus representations are derived equivalent. This yields…
Non-commutative crepant resolutions for some toric singularities II
Špela Špenko, Michel Van den Bergh
Using the theory of dimer models Broomhead proved that every 3-dimensional Gorenstein affine toric variety Spec R admits a toric non-commutative crepant resolution (NCCR). We give…
Positive trace polynomials and the universal Procesi-Schacher conjecture
Igor Klep, Špela Špenko, Jurij Volčič
Positivstellensatz is a fundamental result in real algebraic geometry providing algebraic certificates for positivity of polynomials on semialgebraic sets. In this article Positivs…
Non-commutative crepant resolutions for some toric singularities I
Špela Špenko, Michel Van den Bergh
We give a criterion for the existence of non-commutative crepant resolutions (NCCR's) for certain toric singularities. In particular we recover Broomhead's result that a 3-dimensio…
Generalised Witt algebras and idealizers
Susan J. Sierra, Špela Špenko
Let be an algebraically closed field of characteristic zero, and let be an additive subgroup of . Results of Kaplansky-Santharoubane and Su classify intermediate…
Semi-orthogonal decompositions of GIT quotient stacks
Špela Špenko, Michel Van den Bergh
If G is a reductive group which acts on a linearized smooth scheme then we show that under suitable standard conditions the derived category of coherent sheaves of the correspo…
Comparing the commutative and non-commutative resolutions for determinantal varieties of skew symmetric and symmetric matrices
Špela Špenko, Michel Van den Bergh
Let Y be the variety of (skew) symmetric nxn-matrices of rank less than or equal to r. In paper we construct a full faithful embedding between the derived category of a non-commuta…
Sweeping words and the length of a generic vector subspace of M_n(F)
Igor Klep, Špela Špenko
The main result of this short note is a generic version of Paz's conjecture on the lengths of generating sets in matrix algebras. Consider a generic g-tuple A=(A_1,..., A_g) of nxn…
Non-commutative resolutions of quotient singularities
Špela Špenko, Michel Van den Bergh
In this paper we generalize standard results about non-commutative resolutions of quotient singularities for finite groups to arbitrary reductive groups. We show in particular that…
Free function theory through matrix invariants
Igor Klep, Špela Špenko
In this article we introduce powerful tools and techniques from invariant theory to free analysis. This enables us to study free maps with involution. These maps are free noncommut…
Functional identities on matrix algebras
Matej Brešar, Špela Špenko
Complete solutions of functional identities on the matrix algebra are given. The nonstandard…
A tracial Nullstellensatz
Igor Klep, Špela Špenko
The main result of this note is a tracial Nullstellensatz for free noncommutative polynomials evaluated at tuples of matrices of all sizes: Suppose f_1,...,f_r,f are free polynomia…
Functional identities of one variable
Matej Brešar, Špela Špenko
Let be a centrally closed prime algebra over a characteristic 0 field , and let be the trace of a -linear map (i.e., where is a…
Derivations preserving quasinilpotent elements
J. Alaminos, M. Brešar, J. Extremera +2
We consider a Banach algebra with the property that, roughly speaking, sufficiently many irreducible representations of on nontrivial Banach spaces do not vanish on all squ…
Quasi-identities on matrices and the Cayley-Hamilton polynomial
Matej Brešar, Claudio Procesi, Špela Špenko
We consider certain functional identities on the matrix algebra that are defined similarly as the trace identities, except that the "coefficients" are arbitrary polynomials,…
On Lie and associative algebras containing inner derivations
M. Brešar, Š. Špenko
We describe subalgebras of the Lie algebra $\mf{gl}(n^2)$ that contain all inner derivations of (where and is an algebraically closed field of characteristi…
Maps preserving zeros of a polynomial
J. Alaminos, M. Brešar, Š. Špenko +1
Let $\A$ be an algebra and let be a multilinear polynomial in noncommuting indeterminates . We consider the problem of describing linear maps $ϕ:\A\to \A$ tha…
Lie Superautomorphisms on Associative Algebras, II
Y. Bahturin, M. Brešar, Š. Špenko
Lie superautomorphisms of prime associative superalgebras are considered. A definitive result is obtained for central simple superalgebras: their Lie superautomorphisms are of stan…
Identifying derivations through the spectra of their values
M. Brešar, B. Magajna, Š. Špenko
We consider the relationship between derivations and of a Banach algebra that satisfy $\s(g(x)) \subseteq \s(d(x))$ for every , where $\s(\, . \,)$ stands for t…