The N=2 supersymmetric w1+∞ symmetry in the two-dimensional SYK models

We identify the rank (q(syk) + 1) of the interaction of the two-dimensional N = (2, 2) SYK model with the deformation parameter lambda in the Bergshoeff, de Wit and Vasiliev(in 1991)'s linear W-infinity[lambda] algebra via lambda = 1/2(q(syk)+1) by using a matrix generalization. At the vanishing lambda (or the infinity limit of q(syk)), the N = 2 supersymmetric linear W-infinity(N,N) [lambda = 0] algebra contains the matrix version of known N = 2 W-infinity algebra, as a subalgebra, by realizing that the N-chiral multiplets and the N-Fermi multiplets in the above SYK models play the role of the same number of beta gamma and bc ghost systems in the linear W-infinity(N,N) [lambda = 0] algebra. For the nonzero lambda, we determine the complete N = 2 supersymmetric linear W-infinity(N,N)[A] algebra where the structure constants are given by the linear combinations of two different generalized hypergeometric functions having the A dependence. The weight-1, 1/2 currents occur in the right hand sides of this algebra and their structure constants have the lambda factors. We also describe the lambda = 1/4 (or q(syk) = 1) case in the truncated subalgebras by calculating the vanishing structure constants.