Related papers: Generic algebras with involution of degree 8m

In this paper we show that the fields of rational invariants over the irreducible components of the module varieties for an acyclic gentle algebra are purely transcendental extensions. Along the way, we exhibit for such fields of rational…

Motivated by algebraic structures appearing in Rational Conformal Field Theory we study a construction associating to an algebra in a monoidal category a commutative algebra ({\em full centre}) in the monoidal centre of the monoidal…

Ufnarovski remarked in 1990 that it is unknown whether any finitely presented associative algebra of linear growth is automaton, that is, whether the set of normal words in the algebra form a regular language. If the algebra is graded, then…

We study the existence of some irreducible projective plane curves of degree~$8$ with some prescribed topological type of singularities in the algebraic and symplectic worlds.

Let $k$ be an algebraically closed field of characteristic $p>0$, let G=GL_n be the general linear group over $k$, let g=gl_n be its Lie algebra and let $D_s$ be subalgebra of the divided power algebra of g^* spanned by the divided power…

It is demonstrated that point symmetry algebras of general analytic second order ODEs, not necessary of principal type, can have all dimensions between 0 and 8 except for 7. For the symmetry dimension 8 the ODE must be locally…

Consider complex semisimple Lie algebras of a given dimension specified by their structure constants. We describe a finite collection of rational functions in the structure constants that form a complete set of invariants: two sets of…

Let $k$ be a field of characteristic not equal to $2,3$, $\mathbb{O}$ an octonion over $k$ and $\mathcal{J}$ the exceptional Jordan algebra defined by $\mathbb{O}$. We consider the prehomogeneous vector space $(G,V)$ where $G=GE_6\times…

In this article we study rational Cherednik algebras at $t = 1$ in positive characteristic. We study a finite dimensional quotient of the rational Cherednik algebra called the restricted rational Cherednik algebra. When the corresponding…

Associative algebras with involution over a field of zero characteristic are considered. It is proved that in this case for any finitely generated associative algebra with involution there exists a finite dimensional algebra with involution…

We introduce a class of normal complex spaces having only mild sin-gularities (close to quotient singularities) for which we generalize the notion of a (analytic) fundamental class for an analytic cycle and also the notion of a relative…

We classify the four dimensional perfect non-simple evolution algebras over a field having characteristic different from 2 and in which there are roots of orders 2, 3 and 7.

This paper studies absolute retracts in congruence modular varieties of universal algebras. It is shown that every absolute retract with finite dimensional congruence lattice is a product of subdirectly irreducible algebras. Further, every…

Differential central simple algebras are the main object of study in this survey article. We recall some crucial notions such as differential subfields, differential splitting fields, tensor products etc. Our main focus is on differential…

Let $m$ be a positive integer, $q$ be a prime power, and $\mathrm{PG}(2,q)$ be the projective plane over the finite field $\mathbb F_q$. Finding complete $m$-arcs in $\mathrm{PG}(2,q)$ of size less than $q$ is a classical problem in finite…

Classical affine Lie algebras appear e.g. as symmetries of infinite dimensional integrable systems and are related to certain differential equations. They are central extensions of current algebras associated to finite-dimensional Lie…

An involution of a real commutative algebra $A$ is a real-linear homomorphism $f : A \rightarrow A$ such that $f^2 = \mathrm{Id}$. We show that there are six involutions of the algebra of bicomplex numbers, contrary to the actual number of…

Let $q$ be a quadratic form over a field $F$ and let $L$ be a field extension of $F$ of odd degree. It is a classical result that if $q_L$ is isotropic (resp. hyperbolic) then $q$ is isotropic (resp. hyperbolic). In turn, given two…

An irreducible smooth representation of a $p$-adic group $G$ is said to be distinguished with respect to a subgroup $H$ if it admits a non-trivial $H$-invariant linear form. When $H$ is the fixed group of an involution on $G$ it is…

For any $m = 3 \left( 2n + 1 \right) with \ n \in \mathbb{N^*} ,$ the prime counting function $\pi(m) = 4 + \left \vert A_4(m) \right \vert + 2 \left \vert A_6(m) \right \vert $ where $A_6(m) $ and $ A_4(m) $ are the sets of Twin Primes and…