We present a derivation of the holographic dual of logarithmic negativity in AdS3/CFT2 that was recently conjectured in Phys. Rev. D 99, 106014 (2019). This is given by the area of an extremal cosmic ...brane that terminates on the boundary of the entanglement wedge. The derivation consists of relating the recently introduced Rényi reflected entropy to the logarithmic negativity in holographic conformal field theories. Furthermore, we clarify previously mysterious aspects of negativity at a large central charge seen in conformal blocks and comment on generalizations to generic dimensions, dynamical settings, and quantum corrections.
In this paper, we introduce the notion of k-derivation, generalized k-derivation and k-reverse derivation on gamma semirings, and we give some commutativity conditions on γ-prime and γ-semiprime ...gamma semirings. Also, we give orthogonality for pairs of k-reverse derivations on gamma semirings.
In this paper, a modified load-independent $T$ -stress constraint parameter $\tau *}$ was defined. The $\tau *}$ of specimens with different crack-tip constraint levels at different $J$ -integrals ...was calculated, and its load-independence has been validated. Based on the modified constraint parameter $\tau *}$ and the numerically calculated JaR curves by using the GursonaTvergaardaNeedleman (GTN) model for the SENB specimens with different $a/W$ , the equations of constraint-dependent JaR curves for the A508 steel were obtained. The predicted JaR curves using the equations essentially agree with the experimental and calculated JaR curves. The transferability of the constraint-dependent JaR curves to the CT, SENT and CCT specimens was validated. The results show that the modified constraint parameter $\tau *}$ and the GTN model can be effectively used to derive the constraint-dependent JaR curves for ductile materials.
Proposition (2.2.1) in “On the modules of m-integrable derivations in non-zero characteristic” is false for general finitely generated ideals I of our ambient polynomial or power series ring, but it ...was always used in the original article for principal ideals. Here we prove it under this hypothesis.
There exists a one to one correspondence between higher derivations $\{d_n\}_{n=0}^\infty$ on an algebra $\mathcal{A}$ and the family of sequences of derivations $\{\delta_n\}_{n=1}^\infty$ on ...$\mathcal{A}$. In this paper, we obtain a relation that calculates each derivation $ \delta_n (n \in \mathbb{N})$ directly as a linear combination of products of terms of the corresponding higher derivation $\{d_n\}_{n=0}^\infty$. Also, we find the general form of the family of inner derivations corresponding to an inner higher derivation. We show that for every two higher derivations on an algebra $\mathcal{A}$, the product of them, is a higher derivation on $\mathcal{A}$. Also, we prove that the product of two inner higher derivations, is an inner higher derivation.
In this paper, we investigated the problem of describing the form of higher Jordan triple derivations on trivial extension algebras. We show that every higher Jordan triple derivation on a $ 2 ...$-torsion free $ * $-type trivial extension algebra is a sum of a higher derivation and a higher anti-derivation. As for its applications, higher Jordan triple derivations on triangular algebras are characterized.
We prove new results about generalized derivations on C⁎-algebras. By considering the triple product {a,b,c}=2−1(ab⁎c+cb⁎a), we introduce the study of linear maps which are triple derivations or ...triple homomorphisms at a point. We prove that a continuous linear map T on a unital C⁎-algebra is a generalized derivation whenever it is a triple derivation at the unit element. If we additionally assume T(1)=0, then T is a ⁎-derivation and a triple derivation. Furthermore, a continuous linear map on a unital C⁎-algebra which is a triple derivation at the unit element is a triple derivation. Similar conclusions are obtained for continuous linear maps which are derivations or triple derivations at zero.
We also give an automatic continuity result, that is, we show that generalized derivations on a von Neumann algebra and linear maps on a von Neumann algebra which are derivations or triple derivations at zero are all continuous even if not assumed a priori to be so.
In the present paper, we study simple algebras, which do not belong to the well-known classes of algebras (associative algebras, alternative algebras, Lie algebras, Jordan algebras, etc.). The simple ...finite-dimensional algebras over a field of characteristic 0 without finite basis of identities, constructed by Kislitsin, are such algebras. In the present paper, we consider two such algebras: the simple seven-dimensional anticommutative algebra \(\mathcal{D}\) and the seven-dimensional central simple commutative algebra \(\mathcal{C}\). We prove that every local derivation of these algebras \(\mathcal{D}\) and \(\mathcal{C}\) is a derivation, and every 2-local derivation of these algebras \(\mathcal{D}\) and \(\mathcal{C}\) is also a derivation. We also prove that every local automorphism of these algebras \(\mathcal{D}\) and \(\mathcal{C}\) is an automorphism, and every 2-local automorphism of these algebras \(\mathcal{D}\) and \(\mathcal{C}\) is also an automorphism.
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