A Characterization of Varieties of Associative Algebras of Exponent two

∗The first author was partially supported by MURST of Italy; the second author was par- tially supported by RFFI grant 99-01-00233.It was recently proved that any variety of associative algebras over a field of characteristic zero has an integral exponential growth. It is known that a variety V has polynomial growth if and only if V does not contain the Grassmann algebra and the algebra of 2 × 2 upper triangular matrices. It follows that any variety with overpolynomial growth has exponent at least 2. In this note we characterize varieties of exponent 2 by exhibiting a finite list of algebras playing a role similar to the one played by the two algebras above

Group Gradings on Associative Algebras with Involution

AbstractIn this paper we describe the group gradings by a finite abelian group G of the matrix algebra Mn(F) over an algebraically closed field F of characteristic different from 2, which respect an involution (involution gradings). We also describe, under somewhat heavier restrictions on the base field, all G-gradings on all finite-dimensional involution simple algebras

Lie nilpotence in group algebras

Lie nilpotence in group algebra

On Shirshov bases of graded algebras

We prove that if the neutral component in a finitely-generated associative algebra graded by a finite group has a Shirshov base, then so does the whole algebra.Comment: 4 pages; v2: minor corrections in English; to appear in Israel J. Mat

Building mutual trust: a framework project for implementing EU common standards in legal interpreting and translation

This edited volume addresses the establishment of core competencies for legal interpreters and translators(LITs) in the European common area, guides to core interpreter training curricula, the training of interpreter trainers, guidance for judicial professionals on working through legal interpreters and an extensive training materials resource bank

Nanopore ReCappable sequencing maps SARS-CoV-2 5′ capping sites and provides new insights into the structure of sgRNAs

The SARS-CoV-2 virus has a complex transcriptome characterised by multiple, nested subgenomic RNAsused to express structural and accessory proteins. Long-read sequencing technologies such as nanopore direct RNA sequencing can recover full-length transcripts, greatly simplifying the assembly of structurally complex RNAs. However, these techniques do not detect the 5 ' cap, thus preventing reliable identification and quantification of full-length, coding transcript models. Here we used Nanopore ReCappable Sequencing (NRCeq), a new technique that can identify capped full-length RNAs, to assemble a complete annotation of SARS-CoV-2 sgRNAs and annotate the location of capping sites across the viral genome. We obtained robust estimates of sgRNA expression across cell lines and viral isolates and identified novel canonical and non-canonical sgRNAs, including one that uses a previously un-annotated leader-to-body junction site. The data generated in this work constitute a useful resource for the scientific community and provide important insights into the mechanisms that regulate the transcription of SARS-CoV-2 sgRNAs