In a previous work [AS2] we showed how to attach to a pointed Hopf algebra A with coradical kΓ, a braided strictly graded Hopf algebra R in the category Γ Γ YD of Yetter-Drinfeld modules over Γ. In this paper, we consider a further invariant of A, namely the subalgebra R of R generated by the space V of primitive elements. Algebras of this kind are known since the pioneering work of Nichols. It...

Given an elliptic fibration $f \colon X \to S$ over the spectrum of a complete discrete valuation ring with algebraically closed residue field, we use Hochschild--Serre spectral sequence to express torsion in $R^1f_\ast \mathscr{O}_X$ as first group cohomology $H^1(G,H^0(S^\prime, \mathscr{O}_{S^\prime}))$. Here, $G$ is Galois maximal extension $K^\prime / K$ such that normalization $X \times_S...

This paper studies a fascinating type of filter in residuated lattices, the so-called pure filters. A combination algebraic and topological methods on filters lattice is applied to obtain some new structural results. The notion purely-prime has been investigated, Cohen-type theorem obtained. It shown that spectrum compact sober space, Grothendieck-type demonstrated. proved Gelfand Hausdorff ded...

For a fixed prime p, let H∗(G) denote the mod p cohomology ring of a finite group G, that is, ExtFpG(Fp,Fp) interpreted algebraically and H ∗(K(G, 1); Fp) interpreted topologically. The cohomology ring is a graded commutative Noetherian ring, or equivalently, a finitely generated graded commutative Fp-algebra. Although the ring is not strictly commutative, the usual concepts from commutative ri...

Let G be an abelian group with identity e. R a graded multiplicative hyperring and ? : Igr(R) expansion function of Igr(R), where is the set all hyperideals R. In this paper, we introduce study concepts ?-primary 2-absorbing which are extended classes prime 2- absorbing R, respectively. Moreover, give basic properties these new types investigate relations among structures.

A decade ago, the authors [5] studied Real cobordismMR, anRO(Z/2)graded Z/2-equivariant spectrum discovered by Landweber [9], which is related to complex cobordismMU in the same way as Atiyah’s RealKtheory KR [1] does to K-theory. In particular, the authors computed the RO(Z/2)-graded coefficients of MR. A key step in that computation was the fact that MR is a complete Z/2-equivariant spectrum,...

The algebras of the title are infinite-dimensional graded Lie L=?i=1?Li, over a field positive characteristic p, which generated by an element degree 1 and satisfy [Li,L1]=Li+1 for i?p. In case p=2 such were classified Caranti Vaughan-Lee in 2003. We announce extension that classification to arbitrary prime characteristic, prove several major steps its proof.

Abstract We present a $$q_T$$ q T -resummed calculation of diphoton production at order N $$^3$$ 3 LL $$^\prime $$ ? + NNLO. To reach the primed level accuracy we have implemented recently published t...