  We present the first 100 pc scale view of the dense molecular gas in the
central ~ 1.3 kpc region of the type-1 Seyfert NGC 1097 traced by HCN (J=4-3)
and HCO+ (J=4-3) lines afforded with ALMA band 7. This galaxy shows significant
HCN enhancement with respect to HCO+ and CO in the low-J transitions, which
seems to be a common characteristic in AGN environments. Using the ALMA data,
we study the characteristics of the dense gas around this AGN and search for
the mechanism of HCN enhancement. We find a high HCN (J=4-3) to HCO+ (J=4-3)
line ratio in the nucleus. The upper limit of the brightness temperature ratio
of HCN (v2=1^{1f}, J=4-3) to HCN (J=4-3) is 0.08, which indicates that IR
pumping does not significantly affect the pure rotational population in this
nucleus. We also find a higher HCN (J=4-3) to CS (J=7-6) line ratio in NGC 1097
than in starburst galaxies, which is more than 12.7 on the brightness
temperature scale. Combined from similar observations from other galaxies, we
tentatively suggest that this ratio appears to be higher in AGN-host galaxies
than in pure starburst ones similar to the widely used HCN to HCO+ ratio. LTE
and non-LTE modeling of the observed HCN and HCO+ lines using J=4-3 and 1-0
data from ALMA, and J=3-2 data from SMA, reveals a high HCN to HCO+ abundance
ratio (5 < [HCN]/[HCO+] < 20: non-LTE analysis) in the nucleus, and that the
high-J lines (J=4-3 and 3-2) are emitted from dense (10^{4.5} < n_H2 [/cc] <
10^6), hot (70 < Tkin [K] < 550) regions. Finally we propose that the high
temperature chemistry is more plausible to explain the observed enhanced HCN
emission in NGC 1097 than the pure gas phase PDR/XDR chemistry.
