In this note we show that an one-dimensional algebraic subset V of arbitrarily dimensional polidisc D n , which has the polynomial extension property, is a holomorphic retract.
Motivated by the recent progress of research on extending holomorphic functions defined on subvarieties of classical domains and its connections to the 3-point Pick interpolation, we study a special class of twodimensional algebraic subvarieties Mα of the unit tridisc, defined as the sets
In this work, it is shown that for the classical Cartan domain $$\mathcal {R}_{II}$$
R
II
consisting of symmetric $$2\times 2$$
2
×
2
matrices, every algebraic subset of $$\mathcal {R}_{II}$$
R
II
, which admits the polynomial extension property, is a holomorphic retract.
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