Supplemental Material: A constraint on post–6 Ma timing of western Grand Canyon (Arizona, USA) incision removed: Local derivation indicated by ca. 5.4 Ma fluvial deposits below Shivwits Plateau basalts north of Grand Canyon

<div>Geochronologic data for both clasts and detrital zircon analyses.<br></div>

Supplemental Material: A constraint on post–6 Ma timing of western Grand Canyon (Arizona, USA) incision removed: Local derivation indicated by ca. 5.4 Ma fluvial deposits below Shivwits Plateau basalts north of Grand Canyon

<div>Geochronologic data for both clasts and detrital zircon analyses.<br></div>

Conservative algebras of 2-dimensional algebras, III

In the present paper we prove that every local and 2-local derivation on conservative algebras of 2-dimensional algebras are derivations. Also, we prove that every local and 2-local automorphism on conservative algebras of 2-dimensional algebras are automorphisms.

2-Local derivations of real AW*-algebras are derivation

Abstract2-Local derivations on real matrix algebras over unital semi-prime Banach algebras are considered. Using the real analogue of the result that any 2-local derivation on the algebra $$M_{2^n}(A)$$ M 2 n ( A ) ($$n\ge 2$$ n ≥ 2 ) is a derivation, it is shown that any 2-local derivation on real AW$$^*$$ ∗ -algebra for which the enveloping algebra is (complex) AW*-algebra, is a derivation, where A is a unital semi-prime Banach algebra with the inner derivation property.

2-Local derivations on the W-algebra W(2,2)

This paper is devoted to study 2-local derivations on [Formula: see text]-algebra [Formula: see text] which is an infinite-dimensional Lie algebra with some outer derivations. We prove that all 2-local derivations on the [Formula: see text]-algebra [Formula: see text] are derivations. We also give a complete classification of the 2-local derivation on the so-called thin Lie algebra and prove that it admits many 2-local derivations which are not derivations.

2-LOCAL DERIVATIONS ON SEMISIMPLE BANACH ALGEBRAS WITH MINIMAL LEFT IDEALS

Let ${\mathcal{A}}$ be a semisimple Banach algebra with minimal left ideals and $\text{soc}({\mathcal{A}})$ be the socle of ${\mathcal{A}}$ . We prove that if $\text{soc}({\mathcal{A}})$ is an essential ideal of ${\mathcal{A}}$ , then every 2-local derivation on ${\mathcal{A}}$ is a derivation. As applications of this result, we can easily show that every 2-local derivation on some algebras, such as semisimple modular annihilator Banach algebras, strongly double triangle subspace lattice algebras and ${\mathcal{J}}$ -subspace lattice algebras, is a derivation.

Local and 2-local derivations of solvable Leibniz algebras

We show that any local derivation on the solvable Leibniz algebras with model or abelian nilradicals, whose dimension of complementary space is maximal is a derivation. We show that solvable Leibniz algebras with abelian nilradicals, which have [Formula: see text] dimension complementary space, admit local derivations which are not derivations. Moreover, similar problem concerning [Formula: see text]-local derivations of such algebras is investigated and an example of solvable Leibniz algebra is given such that any [Formula: see text]-local derivation on it is a derivation, but which admits local derivations which are not derivations.

2-Local derivations on Witt algebras

In this paper, we prove that every 2-local derivation on Witt algebras [Formula: see text] or [Formula: see text] is a derivation for all [Formula: see text]. As a consequence we obtain that every 2-local derivation on any centerless generalized Virasoro algebra of higher rank is a derivation.

2-Local derivations of infinite-dimensional Lie algebras

In the present paper, we study 2-local derivations of infinite-dimensional Lie algebras over a field of characteristic zero. We prove that all 2-local derivations of the Witt algebra as well as of the positive Witt algebra and the classical one-sided Witt algebra are (global) derivations. We also give an example of an infinite-dimensional Lie algebra with a 2-local derivation which is not a derivation.