  We report ALMA observations of molecular gas and continuum emission in the 90
and 350 GHz bands toward a nearby Seyfert galaxy NGC 613. Radio continuum
emissions were detected at 95 and 350 GHz from both the circum-nuclear disk
(CND) ($r\leq90$ pc) and a star-forming ring (250 pc $\leq r\leq 340$ pc), and
the 95 GHz continuum was observed to extend from the center at a position angle
of $20^{\circ} \pm 8^{\circ}$. The archival 4.9 GHz data and our 95 GHz data
show spectral indices of $\alpha\leq -0.6$ and $-0.2$ along the jets and in the
star-forming ring; these can be produced by synchrotron emission and free-free
emission, respectively. In addition, we detected the emission of CO(3-2),
HCN(1-0), HCN(4-3), HCO$^+$(1-0), HCO$^+$(4-3), CS(2-1), and CS(7-6) in both
the CND and ring. The rotational temperatures and column densities of molecules
derived from $J=1-0$ and $4-3$ lines of HCN and HCO$^+$ and $J=2-1$ and $7-6$
of CS in the CND and ring were derived. Furthermore, a non-LTE model revealed
that the kinetic temperature of $T_{\rm k}=350-550$ K in the CND is higher than
$T_{\rm k}=80-300$ K in the ring, utilizing the intensity ratios of HCN,
HCO$^+$, and CS. The star-formation efficiency in the CND is almost an order of
magnitude lower than those at the spots in the star-forming ring, while the
dominant activity of the central region is the star formation rather than
active galactic nuclei. We determined that the large velocity dispersion of CO
extending toward the north side of the CND and decomposing into blueshifted and
redshifted features is probably explained by the effect of the radio jets.
These results strongly suggest that the jets heat the gas in the CND, in which
the feedback prevents star formation.
