• Korean Journal of Mathematics
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• v.7 no.1
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• pp.103-110
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• 1999

For a group action ${\alpha}$ on a Kac algebra $\mathbb{K}$ with the crossed product Kac algebra $\mathbb{K}{\rtimes}_{\alpha}G$, we will show that ${\pi}_{\alpha}(\mathbb{K})$ is a sub-Kac algebra of $\mathbb{K}{\rtimes}_{\alpha}G$. We will also investigate the intrinsic group $G(\mathbb{K})$ of $\mathbb{K}$ and get a group action ${\beta}$ on a symmetric Kac algebra $\mathbb{K}_s(G(\mathbb{K})$ with the crossed product sub-Kac algebra $\mathbb{K}_s(G(\mathbb{K}){\rtimes}_{\beta}G$ of $\mathbb{K}{\rtimes}_{\alpha}G$.