The Yangian characters (or q-characters) are known to be closely related to the classical W-algebras and to the centers of the affine vertex algebras at the critical level. We make this relationship more explicit by producing families of generators of the W-algebras from the characters of the Kirillov–Reshetikhin modules associated with multiples of the first fundamental weight in types B and D...

We finish the determination of the invariants of the coadjoint representation of six dimensional real Lie algebras, by determining a fundamental set of invariants for the 99 isomorphism classes of solvable Lie algebras with five dimensional nilradical. We also give some results on the invariants of solvable Lie algebras in arbitrary dimension whose nilradical has codimension one.

‎in this paper‎, ‎using fixed point method‎, ‎we prove the generalized hyers-ulam stability of‎ ‎random homomorphisms in random $c^*$-algebras and random lie $c^*$-algebras‎ ‎and of derivations on non-archimedean random c$^*$-algebras and non-archimedean random lie c$^*$-algebras for‎ ‎the following $m$-variable additive functional equation:‎ ‎$$sum_{i=1}^m f(x_i)=frac{1}{2m}left[sum_{i=1}^mfle...

We study the problem of matrix Lie algebra conjugacy. Lie algebras arise centrally in areas as diverse as differential equations, particle physics, group theory, and the Mulmuley–Sohoni Geometric Complexity Theory program. A matrix Lie algebra is a set L of matrices such that M1,M2 ∈ L =⇒ M1M2 − M2M1 ∈ L. Two matrix Lie algebras are conjugate if there is an invertible matrix M such that L1 = ML...

In [16], Hazrat gave a K-theoretic invariant for Leavitt path algebras as graded algebras. Hazrat conjectured that this invariant classifies Leavitt path algebras up to graded isomorphism, and proved the conjecture in some cases. In this paper, we prove that a weak version of the conjecture holds for all finite essential graphs.

Approximately finite (AF) C *-algebras are classified by approximately finite (r-discrete principal) groupoids. Certain natural triangular subalgebras of AF C *-algebras are similarly classified by triangular subsemigroupoids of AF groupoids [10]. Putting this in a more intuitive way, such subalgebras A are classified by the topologised fundamental binary relation R(A) induced on the Gelfand sp...

Abstract We provide non-isomorphic finite 2-groups which have isomorphic group algebras over any field of characteristic 2, thus settling the Modular Isomorphism Problem.

We analyse extensions $\Sigma$ of groupoids G by bundles A abelian groups. describe a pushout construction for such extensions, and use it to the extension group given groupoid bundle A. There is natural action Sigma on dual A, yielding corresponding transformation groupoid. The this map from fibre product with its Cartesian circle twist over resulting prove that full C*-algebra isomorphic $\Si...

We prove the conjecture of Gaiotto and Rap\v{c}\'ak that $Y$-algebras $Y_{L,M,N}[\psi]$ with one parameters $L,M,N$ zero, are simple one-parameter quotients universal two-parameter $\mathcal{W}_{1+\infty}$-algebra, satisfy a symmetry known as triality. These defined cosets certain non-principal $\mathcal{W}$-algebras $\mathcal{W}$-superalgebras by their affine vertex subalgebras, triality is an...

This paper is a contribution to the isomorphism problem for universal enveloping algebras of finite-dimensional Lie algebras. We focus on solvable small dimensions over fields arbitrary characteristic. prove, an field, that type metabelian algebra whose derived subalgebra has codimension one determined by its algebra. As application results in this paper, we solve dimension four characteristic ...