Jordan operator algebras: Basic theory
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DOI: 10.1002/mana.201700178
Abstract: Jordan operator algebras are norm‐closed spaces of operators on a Hilbert space which are closed under the Jordan product. The discovery of the present paper is that there exists a huge and tractable theory of… read more here.
Keywords: theory; jordan; operator algebras; jordan operator ... See more keywords
Characterizations of the Vertex Operator Algebras VLT${V_{L}^{T}}$ and VLO${V_{L}^{O}}$
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DOI: 10.1007/s10468-016-9644-1
Abstract: In this paper, we give characterizations of the rational vertex operator algebras VLT${V_{L}^{T}}$ and VLO${V_{L}^{O}}$, where L is the root lattice of type A1, T is the tetrahedral group, and O is the octahedral group.… read more here.
Keywords: vlt vlo; vertex operator; algebras vlt; characterizations vertex ... See more keywords
Linear Maps on Standard Operator Algebras Characterized by Action on Zero Products
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DOI: 10.1007/s41980-019-00216-4
Abstract: Let $${\mathcal {A}}$$A be a unital standard algebra on a complex Banach space $${\mathcal {X}}$$X with dim$${\mathcal {X}}\ge 2$$X≥2. The main result of this paper is to characterize the linear maps $$\delta , \tau :… read more here.
Keywords: linear maps; delta; standard operator; operator algebras ... See more keywords
A generalization of intertwining operators for vertex operator algebras
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DOI: 10.1016/j.jalgebra.2017.08.011
Abstract: Abstract For a vertex operator algebra V, we generalize the notion of an intertwining operator among an arbitrary triple of V-modules to an arbitrary triple of N -graded weak V-modules and study their properties. We… read more here.
Keywords: operators vertex; vertex operator; intertwining operators; generalization intertwining ... See more keywords
Hopf actions on vertex operator algebras
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DOI: 10.1016/j.jalgebra.2018.08.012
Abstract: The Hopf actions on vertex operator algebras are investigated. If the action is semisimple, a Schur-Weyl type decomposition is obtained. When the Hopf algebra is finite dimensional and the action is faithful, the action is… read more here.
Keywords: vertex operator; actions vertex; hopf actions; operator algebras ... See more keywords
HEREDITARILY ANTISYMMETRIC OPERATOR ALGEBRAS
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DOI: 10.1017/s1474748019000483
Abstract: Abstract We introduce a notion of ‘hereditarily antisymmetric’ operator algebras and prove a structure theorem for them in finite dimensions. We also characterize those operator algebras in finite dimensions which can be made upper triangular… read more here.
Keywords: antisymmetric operator; operator; operator algebras; hereditarily antisymmetric ... See more keywords
On vertex operator algebras associated to Jordan algebras of Hermitian type
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DOI: 10.1080/00927872.2019.1646267
Abstract: Abstract In this paper, we construct a family of vertex operator algebras parameterized by a non-zero complex number r, whose Griess algebras V2 are isomorphic to Hermitian Jordan algebras of type C and A with… read more here.
Keywords: vertex; operator algebras; vertex operator; jordan algebras ... See more keywords
Lax Operator Algebras and Applications to τ-Symmetries for Multilayer Integrable Couplings
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DOI: 10.3390/sym14061185
Abstract: The algebraic structures of zero curvature representations are furnished for multilayer integrable couplings associated with matrix spectral problems, both discrete and continuous. The key elements are a class of matrix loop algebras consisting of block… read more here.
Keywords: algebras applications; applications symmetries; integrable couplings; lax operator ... See more keywords