Related papers: Z_8 is not dualizable

In this paper, we focus on the duo ring property via quasinilpotent elements which gives a new kind of generalizations of commutativity. We call this kind of ring qnil-duo. Firstly, some properties of quasinilpotents in a ring are provided.…

In discussions of the T-duality between the two heterotic string theories, the duality is actually implemented through the "common" SO(16) x SO(16) subgroup of "SO(32)" and E_8 x E_8. In fact, however, a global investigation shows that no…

In this article we give a characterization of left (right) quasi-duo differential polynomial rings. In particular, we show that a differential polynomial ring is left quasi-duo if and only if it is right quasi-duo. This yields a partial…

The Kaplansky unit conjecture for group rings is false in characteristic zero.

We discuss a general duality principle, between noncommutative analogues of the standard cube $\mathbb Z_2^N$, and nonocommutative analogues of the standard sphere $S^{N-1}_\mathbb R$. This duality is by construction of algebraic geometric…

A computer calculation with Magma shows that there is no extremal self-dual binary code C of length 72 that has an automorphism group containing D10, Z3xZ3, or Z7. Combining this with the known results in the literature one obtains that…

We re-examine the question of heterotic - heterotic string duality in six dimensions and argue that the $E_8\times E_8$ heterotic string, compactified on $K3$ with equal instanton numbers in the two $E_8$'s, has a self-duality that inverts…

A long standing question asks whether $\mathbb{Z}$ is uniformly 2-repetitive [Justin 1972, Pirillo and Varricchio, 1994], that is, whether there is an infinite sequence over a finite subset of $\mathbb{Z}$ avoiding two consecutive blocks of…

We consider a generalization of the quaternion ring $\Big(\frac{a,b}{R}\Big)$ over a commutative unital ring $R$ that includes the case when $a$ and $b$ are not units of $R$. In this paper, we focus on the case $R=\mathbb{Z}/n\mathbb{Z}$…

According to string/fivebrane duality, the Green-Schwarz factorization of the $D=10$ spacetime anomaly polynomial $I_{12}$ into $X_4\, X_8$ means that just as $X_4$ is the anomaly polynomial of the $d=2$ string worldsheet so $X_8$ should be…

We show that the direct sum of an odd number of matrices $$C=\left(\begin{array}{cccc} 0&0&0&1\\ 1&0&0&0\\ 0&1&0&0\\ 0&0&1&1 \end{array}\right)$$ cannot be a sum $P+Q$ of matrices over $\mathbb{F}_2$ satisfying $P^2=P$ and $Q^3=O$.

We answer in negative two of questions posed in [4]. We also establish a new characterization of semiprime left Goldie rings by showing that a semiprime ring R is left Goldie iff it is regular left fusible and has finite left Goldie…

We prove that the ring of Weyl invariant $E_8$ weak Jacobi forms is isomorphic to that of joint covariants of a binary sextic and a binary quartic form. The ring is therefore finitely generated. A minimal basis of generators is obtained…

The notion of (Z/2Z) x (Z/2Z)-symmetric spaces is a generalization of classical symmetric spaces, where the group Z/2Z is replaced by (Z/2Z) x (Z/2Z). In this article, a classification is given of the (Z/2Z) x (Z/2Z)-symmetric spaces G/K…

A general study of non-abelian duality is presented. We first identify a possible obstruction to the conformal invariance of the dual theory for non-semisimple groups. We construct the exact non-abelian dual for any Wess-Zumino-Witten (WZW)…

We prove that Z in definable in Q by a formula with 2 universal quantifiers followed by 7 existential quantifiers. It follows that there is no algorithm for deciding, given an algebraic family of Q-morphisms, whether there exists one that…

In this paper, we compute the number of z-classes (conjugacy classes of centralizers of elements) in the symmetric group S_n, when n is greater or equal to 3 and alternating group A_n, when n is greater or equal to 4. It turns out that the…

The notion of formal duality in finite Abelian groups appeared recently in relation to spherical designs, tight sphere packings, and energy minimizing configurations in Euclidean spaces. For finite cyclic groups it is conjectured that there…

We prove that the knot groups of $6_2$ and $7_6$ are not bi-orderable. These are the only two knot groups up to 7 crossings whose bi-orderability was not known. Our method applies to a very broad class of knots.

A semidualizing module is a generalization of Grothendieck's dualizing module. For a local Cohen-Macaulay ring $R$, the ring itself and its canonical module are always realized as (trivial) semidualizing modules. Reasonably, one might…