On Clifford theory with Galois action

Let $\widehat{G}$ be a finite group, $N$ a normal subgroup of $\widehat{G}$ and $\theta\in \operatorname{Irr}N$. Let $\mathbb{F}$ be a subfield of the complex numbers and assume that the Galois orbit of $\theta$ over $\mathbb{F}$ is invariant in $\widehat{G}$. We show that there is another triple $(\widehat{G}_1,N_1,\theta_1)$ of the same form, such that the character theories of $\widehat{G}$ over $\theta$ and of $\widehat{G}_1$ over $\theta_1$ are essentially "the same" over the field $\mathbb{F}$ and such that the following holds: $\widehat{G}_1$ has a cyclic normal subgroup $C$ contained in $N_1$, such that $\theta_1=\lambda^{N_1}$ for some linear character $\lambda$ of $C$, and such that $N_1/C$ is isomorphic to the (abelian) Galois group of the field extension $\mathbb{F}(\lambda)/\mathbb{F}(\theta_1)$. More precisely, "the same" means that both triples yield the same element of the Brauer-Clifford group $\operatorname{BrCliff}(G,\mathbb{F}(\theta))$ defined by A. Turull.Comment: v3: Referee's comments included, and a few other small correction

Corestriction for algebras with group action

We define a corestriction map for equivariant Brauer groups in the sense of Fr\"ohlich and Wall, which contain as a special case the Brauer-Clifford groups introduced by Turull. We show that this corestriction map has similar properties as the corestriction map in group cohomology (especially Galois cohomology). In particular, composing corestriction and restriction associated to a subgroup $H\leq G$ amounts to powering with the index $\lvert G:H \rvert$.Comment: Typos corrected, final versio

The Schur-Clifford subgroup of the Brauer-Clifford group

We define a Schur-Clifford subgroup of Turull's Brauer-Clifford group, similar to the Schur subgroup of the Brauer group. The Schur-Clifford subgroup contains exactly the equivalence classes coming from the intended application to Clifford theory of finite groups. We show that the Schur-Clifford subgroup is indeed a subgroup of the Brauer-Clifford group, as are certain naturally defined subsets. We also show that this Schur-Clifford subgroup behaves well with respect to restriction and corestriction maps between Brauer-Clifford groups.Comment: Corrected a few typos. Final versio

Lattices of finite abelian groups

We study certain lattices constructed from finite abelian groups. We show that such a lattice is eutactic, thereby confirming a conjecture by B\"ottcher, Eisenbarth, Fukshansky, Garcia, Maharaj. Our methods also yield simpler proofs of two known results: First, such a lattice is strongly eutactic if and only if the abelian group has odd order or is elementary abelian. Second, such a lattice has a basis of minimal vectors, except for the cyclic group of order 4.Comment: v2: Minor corrections due to referee reports, 14 page

Affine Symmetries of Orbit Polytopes

An orbit polytope is the convex hull of an orbit under a finite group $G \leq \operatorname{GL}(d,\mathbb{R})$. We develop a general theory of possible affine symmetry groups of orbit polytopes. For every group, we define an open and dense set of generic points such that the orbit polytopes of generic points have conjugated affine symmetry groups. We prove that the symmetry group of a generic orbit polytope is again $G$ if $G$ is itself the affine symmetry group of some orbit polytope, or if $G$ is absolutely irreducible. On the other hand, we describe some general cases where the affine symmetry group grows. We apply our theory to representation polytopes (the convex hull of a finite matrix group) and show that their affine symmetries can be computed effectively from a certain character. We use this to construct counterexamples to a conjecture of Baumeister et~al.\ on permutation polytopes [Advances in Math. 222 (2009), 431--452, Conjecture~5.4].Comment: v2: Referee comments implemented, last section updated. Numbering of results changed only in Sections 9 and 10. v3: Some typos corrected. Final version as published. 36 pages, 5 figures (TikZ

Your Online Identity as a Researcher

This workshop will help researchers to create an online identity as a way to better disseminate research and to collaborate. Social networks such as ResearchGate and Academia.edu will be introduced as well as Google Scholar profiles, Twitter for research, blogs and the ORCID identifier. Benefits (and where to be careful) Tools ResearchGate, Academia.edu, Google Scholar, LinkedIn Twitter, Facebook Blogs, Personal website ORCID ID and other identifiers Slideshare, figshar

Demystifying Citation Metrics

Attendees will learn about the benefits and limitations of citation analysis. We will also provide help to find metrics such as h-index or Journal Impact Factor in Scopus, Web of Science and Google Scholar. Finally, we will give some advice on the use of metrics on your resume. Pros and Cons (use and benefits, controversy and limitations) Tools (Scopus, Web of Science, Google Scholar) Metrics (H-index, Journal Impact Factor, CiteScore) Altmetrics ORCID ID Metrics for C