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Antisymmetrizing the actions of hand triple contained in volume operator and grasping on the segments rooting through any-valent vortex of spin netwok, and using the binor identity, a proof is given that all these actions are eigenactions with eigenvalue -2. A systematic algebraic method to calculate the eigenvalues of volume operator for any-valent vortices is given, and the general and algebraic expressions of volume eigenvalues for 3-, 4-, 5-, 6- valent vertices are obtained.
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Keywords:
- volume operator /
- any-valent vortex /
- proof of eigenactions /
- spectrum of eigenvalues
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