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Let $\mathcal{O}$ be a complete discrete valuation ring, $\mathcal{K}$ itsquotient field, and $A$ the symmetric Kronecker algebra over $\mathcal{O}$. Weconsider the full subcategory of the category of $A$-lattices whose objects are$A$-lattices $M$ such that $M\otimes_{\mathcal{O}}\mathcal{K}$ is projective$A\otimes_{\mathcal{O}}\mathcal{K}$-modules. In this paper, we study Hellerlattices of indecomposable periodic modules over $A$. As a main result, wedetermine the shapes of stable Auslander--Reiten components containing Hellerlattices of indecomposable periodic modules over $A$.

On periodic stable Auslander-Reiten components containing Heller lattices over the symmetric Kronecker algebra