Related papers: The Ideals of Free Differential Algebras

Noncommutative differential calculus on quantum Minkowski space is not separated with respect to the standard generators, in the sense that partial derivatives of functions of a single generator can depend on all other generators. It is…

Let $A$ be an associative unital algebra, $B_k$ its successive quotients of lower central series and $N_k$ the successive quotients of ideals generated by lower central series. The geometric and algebraic aspects of $B_k$ and $N_k$ have…

Let $(c_k)_{k\in \mathbb{N}}$ be a sequence of positive integers. We investigate the set of $A>1$ such that the integer part of $A^{c_1\cdots c_k}$ is always a prime number for every positive integer $k$. Let $\mathcal{W}(c_k)$ be this set.…

We show how one can construct a differential calculus over an algebra where position variables x and momentum variables p have be defined. As the simplest example we consider the one-dimensional q-deformed Heisenberg algebra. This algebra…

For the algebra $\mI_1= K<x, \frac{d}{dx}, \int>$ of polynomial integro-differential operators over a field $K$ of characteristic zero, a classification of simple modules is given. It is proved that $\mI_1$ is a left and right coherent…

We show that the complicated *-structure characterizing for positive q the U_qso(N)-covariant differential calculus on the non-commutative manifold R_q^N boils down to similarity transformations involving the ribbon element of a central…

If $(G,V)$ is a multiplity free space with a one dimensional quotient we give generators and relations for the non-commutative algebra $D(V)^{G'}$ of invariant differential operators under the semi-simple part $G'$ of the reductive group…

We find conditions on ideals of an algebra under which the algebra is dibaric. Dibaric algebras have not non-zero homomorphisms to the set of the real numbers. We introduce a concept of bq-homomorphism (which is given by two linear maps $f,…

Given a unital associatve graded algebra we construct the graded q-differential algebra by means of a graded q-commutator, where q is a primitive N-th root of unity. The N-th power (N>1) of the differential of this graded q-differential…

In this paper we present an algorithm to compute a Standard Basis for a fractional ideal $\mathcal{I}$ of the local ring $\mathcal{O}$ of an $n$-space algebroid curve with several branches. This allows us to determine the semimodule of…

Statistical independence is a notion ubiquitous in various fields such as in statistics, probability, number theory and physics. We establish the stability of independence for any pair of random variables by their corresponding Brockwell…

The correspondence between commutative rings of ordinary differential operators (ODOs) and algebraic curves was established by Burchnall and Chaundy, Krichever and Mumford, among many others. To make this correspondence computationally…

Consider a random polynomial $$ G_Q(x)=\xi_{Q,n}x^n+\xi_{Q,n-1}x^{n-1}+...+\xi_{Q,0} $$ with independent coefficients uniformly distributed on $2Q+1$ integer points $\{-Q, ..., Q\}$. Denote by $D(G_Q)$ the discriminant of $G_Q$. We show…

We present a general method to deform the inhomogeneous algebras of the $B_n,C_n,D_n$ type, and find the corresponding bicovariant differential calculus. The method is based on a projection from $B_{n+1}, C_{n+1}, D_{n+1}$. For example we…

Let $X$ be a finite connected graph, each of whose vertices has degree at least three. The fundamental group $\Gamma$ of $X$ is a free group and acts on the universal covering tree $\Delta$ and on its boundary $\partial \Delta$, endowed…

In this article, we describe the construction of graded $q$-differential algebra with ternary differential satisfying the property $d^3=0$ and the $q$-Leibniz rule. Our starting point is coordinate first order differential calculus on some…

It is shown that there is an absolute constant $C$ such that any rational $\frac bq\in]0, 1[, (b, q)=1$, admits a representation as a finite sum $\frac bq=\sum_\alpha\frac {b_\alpha}{q_\alpha}$ where $\sum_\alpha\sum_ia_i(\frac…

The non-commutative differential calculus on the quantum groups $SL_q(N)$ is constructed. The quantum external algebra proposed contains the same number of generators as in the classical case. The exterior derivative defined in the…

We study the free (associative, non-commutative) Baxter algebra on one generator. The first explicit description of this object is due to Ebrahimi-Fard and Guo. We provide an alternative description in terms of a certain class of trees,…

Let C be an algebraically closed field and X a projective curve over C. Consider an ordinary linear differential equation, or a linear differ- ence equation, with coefficients in the field of rational functions of X, and assume that its…